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ba b a ba b a b+ ++ + 39. 39. 39. 39. 39. 40 81 130 41 83 91 16 28
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ab ab ab ab ab ab abEJ ERCI CI O 101. 1. 1. 1. 1.7 6 9 47 6 13 9 4
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y x yx x x y y yx y + + 4.4.4.4.4. + + + 6 8 5 6 116 6 13 8 7 5 11
613 7 6m n mn mmm m m nn nm n5.5.5.5.5. + + + + + + + a b b c a c
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81 19 30 6 80 2581 80 0 19 6 25 0 3030x y z y x x yx x x y y y
zz7.7.7.7.7.15 6 8 20 5 3115 8 86 5 12 20 31 118 12 112 2 22 2 2
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0483 4 2 3 4 2 3 33 3 3 3 34 2 4 23a b a b a b a b a b a ba b a b a
b a b a ba b a ba b10.10.10.10.10. + + + + + + + + a b c a b c a b
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cc c c b b b a ax x x x x x x xx x x x x x x x+ + + + + + + ++ + +
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334163412122342 8 3474133162 18 1617634123 24147417614a b a b a ba
a a a a b b b b ba b+ + + + + +17.17.17.17.17. 352110132 23511026 1
2010131021326 1 63131310132 2 22 2 2 2 22m mn m mn mn mm m m m m mn
mn mn mn mnm mn + + + + + + 18.18.18.18.18. + + + + + + +
3412562341613234739 28121912123422 3 84945616135 1 26661912942 2
132 2 22 2 2 22 2 2 2 2 22 2a ab b a ab b b aba a a a ab ab ab ab
abb b b b b ba ab b19.19.19.19.19. 0 4 313806250 21460 4252 250380
23 168148017506142 4 141440 35 31 6 250175 0 35 252 2 3 2 2 32 2 2
2 2 2 2 23 3 3 3 32 3, , ,, ,, ,,,, ,,, ,x y xy y x y xy yx y x y x
y xy xy xy xy xyy y y y yxy y+ + + + + +20. 20. 20. 20.
20.325750351250 215325350 23 15 5251325750125157 2 105015013251501
2 1 2 1 21 1 1 1 1 2 2 2 2 21 2a b a b a ba a a a a b b b b ba bm m
m m m mm m m m m m m m m mm m + ++ + + + +,,EJ ERCI CI O 11Para
resolver los problemasdel 1 al 18 las literales toman los
siguientes valores:a = 1 b = 2 c = 3 m = 1/2 n = 1/3 p = 1/4 a = 1
b = 2 c = 3 m = 1/2 n = 1/3 p = 1/4 a = 1 b = 2 c = 3 m = 1/2 n =
1/3 p = 1/4 a = 1 b = 2 c = 3 m = 1/2 n = 1/3 p = 1/4 a = 1 b = 2 c
= 3 m = 1/2 n = 1/3 p = 1/41.1.1.1.1.3 3 1 2 6 ab 2.2.2.2.2.5 5 1 2
3 5 8 3 1202 3 2 3a b c 3.3.3.3.3. b mn2 2212134623 4.4.4.4.4.24
2412131461271461081182 32 3m n p
_,
_, 5.5.5.5.5. 23231 21223418824134 2 3 4 23a b m
_, 6.6.6.6.6. 712712314121891211612189384631283 2 32c p m
_, 7.7.7.7.7.m n pb c a
_,
_, 121314141271414322 38.8.8.8.8. 5656 11256125121 2 2 13 2a mb
c
_, 9.9.9.9.9.2 223 49 36 62 2bc 10. 10. 10. 10. 10. 4 12 412122
3 2 216 26 122 3 23 3m bc 11.11.11.11.11. mn a b 812138 1
2166486434 3 4 312.12.12.12.12. 434 132341829abc 13.13.13.13.13. 55
212131420141125112602 222b mnp
_,
14.14.14.14.14. 34233422333 842 932441836613232bc
15.15.15.15.15. 22121311911332 2mn
_,
16. 16. 16. 16. 16.2422412132131424621911642114442112416242 2 2
2mnn p
_,
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17.17.17.17.17. 3 6423 642 32123 648729 3 373 248 372 2163 6 3 3
6 333 b cm.18.18.18.18.18.
35321253511423212521235443225023513212535325351526752252323 33
apbbmEJ ERCI CI O 12Para resolver los problemas del 1 al 18 las
literales tomanlos siguientes valores:a =3 b =4 c =1/3 d =1/2 m =6
n =1/41.1.1.1.1.a ab b2 2 2 22 3 2 3 4 4 9 24 16 1 + + +
2.2.2.2.2.c cd d2 22 221321312121913144 12 9362536+ +
_, + +
_, + + + +3.3.3.3.3. acbd+ + + 3134129 8 174.4.4.4.4. cdmn + + +
+ 2131261422324 22 72 636435.5.5.5.5. a b m2 2 2 2 2 23 2
6334266931623663 8 6 1 + + + + 6.6.6.6.6. 351223513124 212152 11 10
5545c b d + + + +7.7.7.7.7. abnacdbdm+ + + + +
341431312412612141122648 213144 6 13149349238.8.8.8.8. b n m + + +
+ + + + + 6 4146 6 21264 1 1221728129.9.9.9.9. c a d b n d 3 16
8133312164148121331216142 1 8122 16 1213262 2 12 + + + + +
10.10.10.10.10. mdab
_,
612216116216 16 345634.1 11 111.1.1.1.1.
344313441461341461121242 12432418222 2cnm+
_,
+
_,
+ + + 12.12.12.12.12. 421621 212814124816112121 1 1 02 2 2 2d
n+
_, +
_, + + 13.13.13.13.13. a bcb md++++ 3 4134 612713101221 20
114.14.14.14.14. b anmbda++ ++ + + + + 54 3146 4125311421215 4 4 15
2315.15.15.15.15. 12216 112133241614361124 384 362181623 4
4824472412324c abn am d+ + + + + 16.16.16.16.16.43366443 336
661693366433664 1 1 4 ba m+ + + + + 17.17.17.17.17. b d c d +++ +
++ 223 844 212231381242 121 2432346 343418.18.18.18.18. 233 242 3
433 21243142 144339443122 123332432243924328983264 9 12861872 2 2 2
2258+ + + +
_,
+ + + + + a b da nEJ ERCI CI O 13Para los problemas 1 al 24 las
literales toman los siguientes valores:a =1 b =2 c =3 d =4 m =1/2 n
=2/3 p =1/4 x =01.1.1.1.1. ( ) ( ) a bc d + + 1 2 3 4 3 3 4 9 4
52.2.2.2.2. ( )( ) ( )( ) a bb a + + 1 2 2 1 3 1 33.3.3.3.3. ( )( )
b m c n a +
_,
_, +
_,
_, + + + + 4 2123234 14 129 234327347247 8215272 2 124. 4. 4. 4.
4.( )( ) ( )( ) 2 3 4 2123234142 1 2 1 4 3 5 152 2m n p b + + +
_, +
_, + + 5.5.5.5.5. ( )( )( ) ( ) ( ) 4 8 6 4128141 2 6234 2 2 3 0
02 2 2 2m pa b n d + + +
_, +
_, + 6.6.6.6.6. ( )( )( )( ) ( )( )( ) c b d c b a m p
_,
_, 3 2 4 3 2 112141 1 12 14147.7.7.7.7. ( ) ( ) ( ) b c d a mn
x2 2 2 2 562 2 3 4 112232 0 4 73 462876168 76161626 + + + + +
_, + +
_, 8.8.8.8.8.( ) ( ) ( ) 2 6 4 2120 62 3 4 4 64 9 4 16 6 13 64
78 64 142 2 2 2 2 2mx b c d + + + + + 9.9.9.9.9.
89168129231614214183424622322 63832 23mnpba +
_, +
_,
+ + + + 10.10.10.10.10.( ) ( ) ( ) x m a d cb c a+ + + + + 0121
4 3121 64 31262 312 3 111.11.11.11.11. ( ) 44121411 2342 141
494345935927552 222 2225m paa bc+++
_,
++
_, + 12.12.12.12.12. ( )( )( )( )( )( )2 3 4 8 6 4 9
2021232341481462341292320141 2 1 2 4 2 6 5 4 4 11 176m n p p n m n
p + + + + + +
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O19Para los problemas 1 al 14 las literales toman los siguientes
valores:a =2 b =3 c =10 x =5 y =4 m =2/3 n =1/51.1.1.1.1. 4 53 6 82
824 8 8 8 0x yx yx yy + + 2.2.2.2.2.x xx xx xx x222225 810 306 5
506 10 7265 105 72 625 50 72150 50 72 172 + + + + + + + 3.3.3.3.3.
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4 8625 28 125 525 16 50 64 256 8625 3500 2000 3200 256 8 3811 + + +
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a b a b ab a a b a b a b ab b + ++ ++ + + + + +26.26.26.26.26. a a
aa a aa ax x xx x xx x+ + + ++ ++ ++1 21 215 64 727.27.27.27.27. m
m mm m m mm m m m m m m m m ma a aa a a aa a a a a a a a a a + + +
+ + 1 22 1 31 2 1 3 1 1 2 334 5 3 85 2 3 8 3 5 2 828.28.28.28.28. a
a a aa a a aa a a a a a a a a a a am m m mm m m mm m m m m m m m m
m m m+ + + + ++ + + + + + + + ++ + + ++ + + + + + + +4 2 12 1 3 14
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aa a a a a a a a a a a a+ + + + + + + + + + + + + 2 1 21 1 32 1 2 1
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n n nn n n n n n n n n n n n+ + + + + + 1 2 3 52 3 5 41 2 3 5 4 1 2
3 4 56 8 195 6 9 811 2 28 8 8 11 2 28EJ ERCI CI O 221.1.1.1.1. b ab
ab a a b + 2 2 2 22.2.2.2.2.2 34x yx yx y+ ++3.3.3.3.3. + + +7 552
5 2 5aa ba b a b4.4.4.4.4. + + + + + +xx xx x x x222 2652 6 5 2 5
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++ + + +3 4 52 3 4 3 2 4n m pn m pn m p m n p9.9.9.9.9. x y zx y zx
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2b ab ab ab ab ab a a ab b11.11.11.11.11. + + + +5 636 92 22 22m n
mnm n mnm mn12.12.12.12.12. + + + + + + 8 5 468 6 10 8 6 10232 3 3
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+ +16.16.16.16.16. 6 8 66 46 8 7 6 43 2 22 33 2 2 3x x y xyxy yx x
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y x y x y x y xy y7 5 2 4 3 2 54 3 2 5 7 3 4 67 5 2 4 3 2 5 7 3 4
67 5 2 4 3 3 4 2 5 6 73 35 8 6060 90 503 95 7 60 90 503 95 90 7 50
60 + ++ + + + + + + + +26.26.26.26.26.a aa a aa a a aa a a ax xx x
xx x x xx x x x+ ++ ++ + ++ + + + + + + 3 11 23 1 23 2 18 55 63 5
63 6 527.27.27.27.27. + + + + + + + 8 16 157 5 815 16 10 815 8 10
164 2 32 3 14 2 11 2 4a a a aa a a aa a a aa a a an n n nn n n nn n
n nn n n n28.28.28.28.28.15 5 6 419 18 3115 14 6 59 3115 14 31 6
593 2 12 1 1 43 2 1 1 44 3 2 1 1x x x xx x x xx x x x x xx x x x x
xa a a aa a a aa a a a a aa a a a a a+ + + + ++ + + ++ + + + + ++ +
++ + + + + +29.29.29.29.29. 9 21 26 145 12 814 33 26 14 814 33 26 8
141 2 3 51 2 41 2 3 5 41 2 3 4 5a a aa a a aa a a a aa a a a am m m
mm m m mm m m m m mm m m m m m + + + + + + + + + + + +30. 30. 30.
30. 30. + ++ + + + + ++ + + + + + + + + 15 50 14 6 823 615 23 56 14
5 83 1 1 24 2 1 14 3 2 1 1 2m m m m mm m m mm m m m m m mx x x x xx
x x xx x x x x x xEJ ERCI CI O 231.1.1.1.1. 112 + +aa2.2.2.2.2. 088
+ +aa3.3.3.3.3. + 93 53 4 3 422 2a aa a a a4.4.4.4.4. + + + 165 165
522 2xy xxy x x xy5.5.5.5.5.11 13 2 23 2 2 3 2 2 + + + +a a b aba a
b ab a a b ab6.6.6.6.6.xx x y xyx x y xy33 2 23 2 28 62 8 6+ ++
+7.7.7.7.7. aa b ab ba a b ab b32 2 33 2 2 38 68 6+ ++ +8.8.8.8.8.+
+ + +yx y x y xyx y x y xy y43 2 2 33 2 2 3 45 7 85 7 89.9.9.9.9.mm
am a m a mam am a m a ma44 3 2 2 3 44 3 2 2 3 45 18 74 18 7 + + +
+10.10.10.10.10.161430 30 + + +b a c db a c d a b c
d11.11.11.11.11. xxy yx xy y x xy y222 2 2 211 1 12.12.12.12.12. aa
b ab ba a b ab b32 2 33 2 2 365 85 8 6+ + + +13.13.13.13.13. x yx y
xyx x y xy y3 32 23 2 2 35 17 55 17 5++ ++ + +14.14.14.14.14. xx y
x y xyx x y x y xy43 2 2 34 3 2 2 319 8 159 8 15 1 + + + +
15.15.15.15.15. a ba b a b a b aba a b a b a b ab ba a b a b a b ab
b5 54 2 3 3 2 45 4 2 3 3 2 4 55 4 3 2 2 3 4 511 2 8 411 2 8 411 8 2
4++ ++ + + + + +16.16.16.16.16. x xx xx x x x4 234 3 2505 255 25
50+ + + + + +17.17.17.17.17. y yy y y yy y y y y yy y y y y y65 4 3
26 5 4 3 26 5 4 3 2419 17 1841 9 17 189 17 18 41+ + + + + +
18.18.18.18.18. a a b a ba b a b ab ba a b a b a b a b ab b6 4 2 2
45 3 3 5 66 5 4 2 3 3 2 4 5 6915 17 1415 9 17 14+ ++ + ++ + + +
+19.19.19.19.19. x x xx xx x x x x x x x4 324 3 2 4 3 2115 3416 34
16 34+ + ++ + + + + +20.20.20.20.20. mm n mn nm m n mn n32 2 33 2 2
317 37 3 1 + + EJ ERCI CI O 241.1.1.1.1. 121413252 14132534132522
22 22 2aa ab ba ab ba ab b+ ++ + 2.2.2.2.2. 154523594523135
594523140945231559 + ++ + +xy yzxy yzxy yzxy yz3.3.3.3.3.
3516342918 530342934133029bcbc ab cdbc ab cdab bc cd + ++ + +
+4.4.4.4.4. 12234529125 8106 29123108912a ba ba ba b +++
+5.5.5.5.5. 5938110573115930 8805731159388057311595719403112 222 22
22 2x yy xyx y xyx y xyx xy y ++ + + +6.6.6.6.6. 56291512385610
945123856123819453 33 2 23 3 2 23 2 2 3m nn m n mnm n m n mnm m n
mn n++ + +++ + +7.7.7.7.7. 37133551412186 5142 361141635182 2222 2a
ab ba aba aba ab b+ ++ +8.8.8.8.8. 385611035310215 244050 18601
20103940686021103940171521102 22 22 22 2 2 2x xy yx xy yx xy yx xy
y x xy y+ + ++++ + + 9.9.9.9.9. a a aa aa a aa a a3 223 23
25678910788 7810 91020 21241581910124+ ++ ++++ + 10 .10 .10 .10 .10
. m mn nmn n m nm mn n m nm m n mn n3 2 32 3 23 2 3 23 2 2
371247595211821 20364 775211852113611718+ + ++++ + + +
+12.12.12.12.12. 123578897201819781212 7207 188
197812192088997812192078a b c db c da b c da b c da b c d+ ++ +
+++++ + + + + 6.6.6.6.6. 58141378656582 781
183565898193565658981932 22 32 2 32 2 33 2 2a b abab aa b ab aa b
ab aa a b ab+ + +++ + + + 7.7.7.7.7. 211514136782921120 49563
29621129565963 2 2 34 2 2 34 3 2 2 34 3 2 2 3m n m n mnm m n mnm m
n m n mnm m n m n mn+ + ++ +++ + + 8.8.8.8.8. + + + + ++ +++ + + +
+ 78114231371237182912781 614238 32463
291278514231124659127851423112474 3 2 2 3 45 3 2 45 4 3 2 2 3 45 4
3 2 2 3 45 4 3 2 2 3 4 29x y x y x y xyx x y xyx x y x y x y xyx x
y x y x y xyx x y x y x y xy1.1.1.1.1.3856569 202456112456222 2a
aaa a a a 2.2.2.2.2. 8 6 5123516 1230 3551523355a ba ba b a b+ +++
+ 3.3.3.3.3. x x yx yx x y x x y3 223 2 3 2236796 796196+ +
4.4.4.4.4.a b ca b ca b c a b c+ + +++ + 1234232 124 343
231274535.5.5.5.5. 2356122 335 661 22131632m n pm n pm n p m n p+ +
++++ +11.11.11.11.11. 353457235813563 55345815 7214 56253458821164
3 3 44 2 2 3 44 3 2 2 3 44 3 2 2 3 4x x y xy yx x y xy yx x y x y
xy yx x y x y xy y+ + + + + + EJ ERCI CI O 259.9.9.9.9.
79231821379111796 791811 1112 13137913918121115135 4 2 3 3 2 4 5 66
4 2 2 4 5 66 5 4 2 3 3 2 4 6 6 5 4 2 3 3 2 4 6x y x y x y x y xy yx
x y x y xy yx x y x y x y x y y x x y x y x y x y y+ + + + + + ++
+++ + + +10.10.10.10.10. 1379587112523163461 2314 3185 687112
3051118187113253 2 2 33 2 23 2 2 3 3 2 2 3x x y xy yx x y xyx x y
xy y x x y xy y + + ++ + 11.11.11.11.11. 310375921372051413352136
7206 5145 39352131320111429354 2 2 4 66 4 2 2 4 66 4 2 2 4 6 6 4 2
2 4 6m n m n nm m n m n nm m n m n n m m n m n n ++ ++++++ + +
+12.12.12.12.12. 387227121213355115634313387 10227 1012123413
93935381722171212342239355 4 3 2 2 3 54 3 2 4 55 4 3 2 2 3 4 55 4 3
2 2 3 4 5c c d c d c d dc d c d cd dc c d c d c d cd dc c d c d c d
cd d+ + + + + +++++ + + + + EJ ERCI CI O 26Para los problemas 1 al
14 las literales toman los siguientes valores:a =1 b =2 c =3 x =4 y
=5 m =3/2 n =2/51.1.1.1.1. a abab ba ab b222 22 2341 4 1 2 2 1 8 4
11 2.2.2.2.2. a bb a b aba b a b ab a a b ab b3 33 2 23 3 2 2 3 2 2
33 2 2 32 5 63 5 6 5 6 31 51 2 61 2 3 2 1 52 64 3 81 10 24 24 11++
+ + + + + + + + + + + 3.3.3.3.3. 1212531 221253121253121122533121
51 2 10272312aa b ca b c a b c + + + + + + 4.4.4.4.4. 3 510 82 15 8
2 8 1523283225152529448103459224512545 48 241027102 22 22 2 2 22 2m
nm n mnm n mn m mn n
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44 3 2 2 3 418 1516 6 916 18 6 64 164 5 18 4 5 64 5 6 5256 8064
1816 25 24125 6 625256 5120 7 200 3000 3750 4 926 ++ + + + + + + +
+ + + + + . . . . .6.6.6.6.6. a am mam m a ma am m a m a a m am m3
2 32 3 23 2 3 2 3 2 2 33 22 375 5 82 6 8 8 2 61 8 1322
132632124229462781 12928144 48 18 814194 ++ + + +
_, +
_, + + +7.7.7.7.7. 237815161104 167 882
110121811012118121102122841012142510 5 8203202 22 22 2 2 22 2a ab
ba ab ba ab b a ab b+ ++ 8.8.8.8.8. 2334121614124 163
145632563225322527856182032425278341250675 150 482008732002 2 32 2
3 32 2 3 3 2 23 2 2m n mn nm n mn n mm n mn m m m n mn+ + + +++++ +
+
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54 2 3 35 4 2 3 3 2 4 55 4 2 3 3 2 4 5355 31 1 2 51 2 312 21 4 5 8
316 32 1 4 40 48 32 21 + + + + + + + + + + 10.10.10.10.10. + + + +
ab mn mxabab mn mx10 81516 10 816 1 2 103225832432 6 48
7411.11.11.11.11.aa b ab ba a b ab b32 2 33 2 2 33 2 2 311 911 91
111 2 9 1 2 21 22 36 8 7 + + + + 12.12.12.12.12.
16423563816423563816442345643843232063896 256 80 924231247789424 24
258xx xx x x + + + + + 13.13.13.13.13.x x y xyx xy yx x y xy yx x y
xy y3 2 23 2 33 2 2 33 2 2 33 2 2 33162534351254 343162
3512514316151251443164 515451255146415161645251252516 15 20 5 56+ +
++ + + + += + + + = + + += + + + =EJ ERCI CI O 271.1.1.1.1. + + ++
+ab b aa b a ab ba ab b ab b2 22 2 2 22 2 25 44 42.2.2.2.2. aa+ + 8
16 1414 133.3.3.3.3. ++ + + + + x xyx y yx x y xy yx yx x y xy yx x
y xy y3 22 33 2 2 323 2 2 33 2 2 3455 475 412 44.4.4.4.4. + + + 3 4
53 4 5 44 5 43 2 3 43 2 3 33 4 3m n mn n mm n mn n nn m
n5.5.5.5.5.8 9 3 67 9 35a b c aa b c aa a+ + 6.6.6.6.6.a b c a b ca
b c aa a b c + + + + 2214. 14. 14. 14. 14. 255692 555
546354961351496113549630 18 245302573081 3 21 3 21 31 34 4 1 4
31730a a a aa a aa a aa a ax x x xx x xx x xx x x + + + + += + = +
= + += =7.7.7.7.7. + + + + +m n p mn pm n p mnpm n p2 2
208.8.8.8.8. 9 5 39 7 25 25 66 25 24 5 32 2 22 2 2 22 2 2 2ax a x
ax aax a x x aa x x ax a + + + + 9.9.9.9.9. 5 6 4 12 8 6 2 5 2 22 5
2 2 5 2 32 33 3 23 2 3 2a a aa a a a aa a a a a a+ + + + + +
10.10.10.10.10. 5 9 4 111 7 6 11 2 9 6 411 2 9 6 4 12 2 9 6 53 2 44
3 4 3 24 3 2 4 3 2x x xx x x x x x xx x x x x x x x + + + + + + + +
11.11.11.11.11. 35 7 117 35 8 6 7 57 5 8 52 2 3 33 2 2 3 23 2 3 2
3a b ab a ba a b ab a aba ab a ab b + + + + + + +12.12.12.12.12. +
+ + + + + + + + + 11 14 25 819 6 9 411 19 8 16 47 411 19 8 16 411
26 8 20 44 23 24 3 25 34 3 25 4 3 2n n nn n nn n n nn n nn n n nn n
n n n13.13.13.13.13. + + + + + + + + + + +6 5 67 5 11 67 11 11 5 6
687 11 11 5 6 66 11 3 5 7 63 34 3 2 2 44 3 2 2 3 44 2 2 44 3 2 2 3
44 3 2 2 3 4a m ama a m a m ma a m a m am ma a m ma a m a m am ma a
m a m am m14.14.14.14.14. + + + + + + ++ + ++ + +4 13 96 8 26 4 8
13 8 230 406 4 8 13 8 27 4 38 13 48 34 2 3 45 3 2 4 55 4 3 2 2 3 4
55 3 2 4 55 4 3 2 2 3 4 55 4 3 2 2 3 4 5x y x y xyx x y xy yx x y x
y x y xy yx x y xy yx x y x y x y xy yx x y x y x y xy
y15.15.15.15.15. a b aa b a ba b+ +22216.16.16.16.16.8 9 8 6 46 5
28 6 4 8 6 6x x yyx y x y+ + ++ + + +17.17.17.17.17. x y x xy yxy y
yx xy y x xy y2 2 2 22 22 2 2 26 7 347 40 9 167 34 7 43 16 + + + +
18.18.18.18.18. 4 8 5 57 6 45 22 2 2 22 2 2 22 2 2 2a ab b a ab ba
ab b a ab ba ab b a b+ + + + ++ + +19.19.19.19.19.x yx y xyx x y xy
yx x y xy yx yx x y xy y3 32 23 2 2 33 2 2 33 33 2 2 314 514 514 53
194 14 5 20 + + + + 20.20.20.20.20.x x y y x x y yx y y x x y yx x
y y4 2 2 4 4 2 2 42 2 4 4 2 2 44 2 2 46 2 328 31 2 322 32 0 + ++ +
+ +21.21.21.21.21. + ++ + + + + + + + + 67 8 66 7 8 66 7 8 63 8 196
4 15 8 255 4 23 25 4 35 4 36 4 36 5 4 3n n nn n nn n n nn n n nn n
nn n n n n22.22.22.22.22. a a b aba b a b ab ba a b a b ab ba a b a
b ab ba b a b ba a b a b a b ab b5 3 2 44 3 2 4 55 4 3 2 4 55 4 3 2
4 54 2 3 55 4 3 2 2 3 4 53 622 10 1122 7 522 7 55 717 7 7 5 2 ++ +
+ + + + + + + + 23.23.23.23.23. 4 5 2 3 5 6 47 8 4 53 5 6 4 3 5 6
13 2 3 23 43 2 4 3 2m m m m m mm m mm m m m m m m + + + + + + +
24.24.24.24.24. 7 11 2 87 11 8 42 8 2 42 2 22 22 2a ab b ba ab bb b
+ + + + 25.25.25.25.25. 3 4 57 8 11 5 6 2 112 7 25 6 2 11 6 7 11a b
ca b a b ca b c a b ca b c a b + + + + + + + + 26.26.26.26.26. 5 14
19 89 13 15 17 10 63 52 8 17 10 13 254 25 4 3 24 35 4 3 2a a aa aa
aa a a a aa aa a a a a+ ++ + + + + + + + +27.27.27.27.27. m m n nm
n m n mn nm m n m n mn nm m n mn nm m n m n mn nm m n m n mn n4 2 2
43 2 2 3 44 3 2 2 3 44 2 2 3 44 3 2 2 3 44 3 2 2 3 410 1511 14 311
4 3 166 7 811 4 3 165 11 11 11 17+ + + ++ + + + + + + +
28.28.28.28.28. a a b ab ba b a b ab ba b a b aba a b a b a b ab ba
a b aba a b a b a b ab ba a b a b a b ab b5 3 2 4 54 2 3 4 53 2 2 3
45 4 3 2 2 3 4 55 2 3 45 4 3 2 2 3 4 55 4 3 2 2 3 4 54 87 15 25 33
57 3 18 22 23 6 21 67 3 18 22 22 7 3 24 2 6+ + + + + + + + + + + +
EJ ERCI CI O 2829.29.29.29.29. x yx y x y x y yx x y x y x yx x y x
y x y xy yx x y x y x yx y x y xy y5 54 3 2 2 3 55 4 3 2 2 35 4 3 2
2 3 4 55 4 3 2 2 34 3 2 4 53 21 183 21 1832 26 18 23 21 1829 47 2++
+ + + ++ + + +30.30.30.30.30. 3 6748 7 1248 7 5 1311 21 22 1 11 22
1 1 2a aa a aa a aa a a aa a aa a a a ax xx x xx x xx x x xx x xx x
x x x+ + + + + + + + + + 6.6.6.6.6. a x x a x ax xa ax a a x ax xa
a x ax x a a x ax xa a x ax xa a x ax xa x ax2 3 2 2 33 2 3 2 2 33
2 2 3 3 2 2 33 2 2 33 2 2 32 23 5 11 113 4 6 83 3 9 17 33 39 17 310
14 + + + ++ + + + + + +7.7.7.7.7. x xx x x x xx x x xx x x x x x x
xx x x xx x x xx x x x4 23 3 24 2 44 3 2 4 3 24 3 24 3 24 3 233 5 7
8 3 45 4 32 4 2 7 8 3 12 4 27 8 3 16 12 4 1+ + + + + + + + + + + +
+ + + +1.1.1.1.1.x x x xx xx x x x2 22 25 4 2 12 6 6 22 1 2 2 3+ +
+ + + 2.2.2.2.2. 3 5 7 4 6 23 8 3 7 7 34 6 2 7 7 3 3a b c a b a b
ca b c b c a b ca b c a b c a b c + + + + + +3.3.3.3.3. x x x xx x
x x x xx x x x x x x3 3 23 2 2 23 2 2 3 21 9 4 6 85 7 3 1 3 8 56 8
3 8 5 6 2 8 3+ + + + + + + + + +4.4.4.4.4. a a a aa a a aa a a a a
a a a2 4 3 23 43 2 4 4 3 21 21 2+ + + + + + + 5.5.5.5.5. ab bc ac
ab bc ac ab bc acbc ac ab bc ac ab acab bc ac ab ac ab bc+ + + + +
+ + + + 5 3 4 6 9 97 8 9 3 5 4 96 9 9 4 9 3 6 98.8.8.8.8. m nm n m
n mn m m n m n mn nm m n n m n mn m m n mnm n m n mn n m m n mn m m
n m n mn n4 43 2 2 3 4 3 2 2 3 44 2 2 4 2 2 3 4 2 2 33 2 2 3 4 4 2
2 3 4 3 2 2 3 417 4 7 6 17 2 7 816 80 4 217 2 7 81 2 17 3 8 81 2 +
+ + + + + + + + + 9.9.9.9.9.+ + + + + + + + + + + + + + +a aa a a a
a a a a a a aa a a a a a a a aa a a a a a a a a a a a a35 4 2 4 3 2
5 4 3 22 3 2 4 3 25 4 3 2 4 3 2 5 3 276 8 4 11 10 275 11 26 16 8 7
15 12 7 7 1511 10 27 12 7 7 15 11 4 3 4210.10.10.10.10. 3 3 20 11
811 9 14 19 8 9 3 11 8 143 11 8 14 20 11 8 17 142 2 2 2 2 22 2 2 2
22 2 2 2 2x y x xy y x xy yxy y x xy y x xy yx xy y x xy y x + + +
+ + + + +11.11.11.11.11. a aa aaa a + + +1 31 40 3 82 122
12.12.12.12.12. a ab ba ab b a ab b a ab ba ab b ab b a ab ba ab b
a ab b ab b2 22 2 2 2 2 22 2 2 2 22 2 2 2 23 8 7 9 3 45 11 17 8 7 2
92 9 4 5 + + + + + + + + + +13.13.13.13.13. mm m m m m m mm m m m m
m m mm m m m m m m m m m m43 2 5 5 4 22 4 2 4 3 24 3 2 5 4 2 5 4
318 6 5 16 16 7 197 1 16 7 3 7 13 57 13 5 16 7 19 17 13 24 + + + +
+ + + + + + + + 14. 14. 14. 14. 14. x yx y x y x y y x y x y xy x x
y x y x y xy yx y xy xy x y x y xyx x y x y x y xy y x y x y xy x x
y x y x y xy y5 54 3 2 2 3 5 4 3 2 4 5 4 3 2 2 3 4 53 2 4 4 4 3 2
45 4 3 2 2 3 4 5 4 3 2 4 5 4 3 2 2 3 4 52 5 7 3 7 11 2 2 7 6 4 87 6
8 1 7 10 12 2 7 6 4 8 7 10 1 9 7 4 4 7 + + + + + + + + + + + + + +
+ + +15. 15. 15. 15. 15. + + + + + + + + + + + + + + + + + + + + +
+a a aa a aa a a a a a a a a a aa a a a a a a a a a a a aa a a a a
a a a a a a a a a a a6 45 3 24 3 4 2 5 4 3 23 2 5 3 2 6 5 4 3 26 5
4 3 2 5 4 3 2 6 5 4 37 83 11 46 11 2 8 3 7 8 5 5 3 7 48 58 135 5 4
1 5 7 41 50 8 3 5 4 14 133 5 4 14 13 5 3 7 48 58 13 8 4 2 44244
a16.16.16.16.16. a a x a x xa x a x ax a x a x a xa x ax x aa a x a
x a x ax x a a x a x a x xa a x a x a x xa a x a x a x ax x5 3 2 3
2 54 2 3 4 4 3 2 2 33 2 4 5 55 4 3 2 2 3 4 5 5 4 3 2 2 3 55 4 3 2 2
3 55 4 3 2 2 3 4 57 9 18 4 820 21 19 9 17 119 7 80 3620 2 21 26 71
9 11 4 289 11 4 2820 2 21 26 7111 + + + ++ + + + + + + + + + + + +
+ +a x a x a x ax x4 3 2 2 3 4 510 26 5 99 + +1.1.1.1.1. a b aa b a
ba b a ba b a b+ + ++ = + = 1234233413543 232 349
412541354512542.2.2.2.2. 38612355635563538656353863 56386433863 23
2 3 23 2 33a a aa a a a aa a a a aa a + + + + + + += +3.3.3.3.3.a b
a ba b a ba b a ba b a b+ + + + ++++++= + + = + +3357362523615165
259 2363 1514 16635736255264.4.4.4.4. 133715114296136 114291
30513514293155613514293155 2651429315765142963 223 23 233 23 23 2
15x xx xx x xx x xxx x xx x xx x x + + ++= + + + ++ + = + +
EJERCICIO 295.5.5.5.5. 7127123725637256341513712372567 91237251518
13433725151734 4 3 23 2 44 3 2 4 3 24 3 2a a a aa a a aa a a a a a
aa a a a + + + + + + = + 6.6.6.6.6. + + + +++ + += + + = +
122314592519253125913203126 195 82031213202 155125913203121320175x
y z yy z x y zx y z x zx y z x z7.7.7.7.7. + ++= + ++ +323418562312
189 10123 2311811213121311811213121181122 2 32 2 32 2 32 2 33 32 2
33 2 2a b ab ba b ab ba b ab ba b ab ba ba b ab ba a b ab8.8.8.8.8.
1229231512193513355911019110122 39356 592 110126
1101219351911012710a b b c a b cb c b c b ca b c b c a ca b c b c a
c + + ++= + = + = 9.9.9.9.9.
131815142314131940231835341101329401813194034110135 2440342 1101310
2940232 188 91210 8801319403411013194023181122801121403 2 2 3 22 3
2 3 23 2 3 23 2 3 2a a a a a a aa a a a a a aa a a a a a aa a a a a
a a a+ + + + + + + ++ ++= + = + = + = +10.10.10.10.10.
35562929192335731361232131417452293212357319143510 18122 391410
17451 2294 961239 2182 14352812191427452191361237182 2 2 2 2 22 2 2
2 22 2 2 2 22 2 2 2 2x xy y x xy y x xy yxy y x xy y x xy yx xy y x
xy y yx xy y x xy y y + + + + + + +++++++++= + = = += + =
34357319143573136122 2 2 2x xy y x xy y11.11.11.11.11.
27151214153438327103438110541832122734381102734382 1102 542 18322
5102715 1107102734381103 3 2 2 2 2 32 2 3 2 2 3 3 2 2 33 2 2 3 2 2
3 3 33 2 2 3a b a b ab a b ab ba b ab b a b ab b a a b ab ba a b ab
b a b ab b a ba a b ab b + + + + + + + + ++ + = + = + = =
34383271027141071027757102 2 3 3 3 3 3a b ab b a b a
b12.12.12.12.12. 131427352553514251147201423514141160144 11412
72020 24 1560143 5 231411601425514520116014032 2 3 44 3 2 2 4 4 44
3 2 2 4 4 3 2 2 34 3 2 2 3 4 3 2 2 3 44 3 2 2 3m n mn nm m n m n n
m nm m n m n n m m n m n mnm m n m n mn n m n m n mn nm m n m n mn
n + + + ++++ + + + = + + 44 3 2 2 351414116014= + + m m n m n
mn13.13.13.13.13. 1213341625145121338121312730141338124 9125 12301
241338121312730141340 381213127301413381213127301413378x yy zz mm n
x y z m nx y z m n x y z m nx y z m n x y z m n++ + + + ++++ + + +=
+ + + + = + +14.14.14.14.14.
5612352338538341623112411212152331639403111123820 9246 9 2124 1624
15 3940165 22 93311 2424121216
9926411241123604015233112411212152334 324 3 2 4 3 23 4 34 3 2 4 24
3 2 4 3 2a a aa aa a a a a aa a a aa a a a a aa a a a a a a+ + + ++
+ + + + ++ + + += + = + =. +13241211172644 2a a.EJERCICIO
301.1.1.1.1. x xx x xxRta x x x3 23 23 253 5 63 63 11 + + + + + .4.
4. 4. 4. 4.x xx x xxRta x x x3 23 23 24 84 1354 13 + + + + .
7.7.7.7.7. 5 8 114 8 115 8 113 2 33 33 23 2 3a ab ba ba abRta a ab
b+ ++ + .2.2.2.2.2. + + + ++ + + +5 9 65 9 6 8 98 95 9 6 8 9a b ca
b c xxRta a b c x .5. 5. 5. 5. 5. m mn nm m n mn nm nRta m m n mn
n4 3 44 2 2 3 42 24 2 2 3 43 64 3 6 84 84 3 6 8 + + + + + .8. 8. 8.
8. 8. 1213412134x yx y +3.3.3.3.3. a ba a b ab ba b ab bRta a a b
ab b3 33 2 2 32 2 33 2 2 38 5 38 5 48 5 3 + + + .6. 6. 6. 6. 6.4 5
5 25 4 84 9 64 5 5 23 2233 2x x xx xx xRtax x x+ + ++ . Rta x y
.12134 9.9.9.9.9. 5 7 85 7 8 115 7 8 12 22 22 2x xy yx xy yRta x xy
y + + + + + + .10. 10. 10. 10. 10. nm m n mn nm m n mn nm m n mn
nmRta m m n mn n33 2 2 33 2 2 33 2 2 333 2 2 39 8 59 8 5 210 8 5
210 8 5 2 + + + + + + .11. 11. 11. 11. 11. 05 85 8033 + + a aa
aRta.EJERCICIO 311.1.1.1.1.( ) x x yx x yy = += 6.6.6.6.6.( ) ( ) a
a b a ba a b a ba a a+ + += + += = 2 11.11.11.11.11.( ) ( ) x y x y
z x y zx y x y z x y zx y z+ + + + = + + + += + 22.2.2.2.2. ( ) x x
xx x xx2 22 23 53 53 5+ += += + 7.7.7.7.7.a b a a ba b a a ba a a2
2 2 2 22 2 2 2 22 2 2223 2+ + = + += = 12.12.12.12.12.( ) ( ) ( ) a
b a a b a ba b a a b a bb + + + += + + =2223.3.3.3.3.( ) a b aa b
aa b+ += + + = + 2 32 33 3 8.8.8.8.8.{ } { } 2 1 32 1 31 3 4a x a a
xa x a a x + + = + + += + = 13. 13. 13. 13. 13.( ) ( ) [ ] + + + +=
+ + + + = + +x y xy x xy y xyx y xy x xy y xyx xy y2 2 2 22 2 2 22
22 32 33 3 24.4.4.4.4. ( ) 4 24 26m mnm mnmn = + += + 9. 9. 9. 9.
9. ( ) [ ] x y x xy y x yx y x xy y x yx xy y2 2 2 2 2 22 2 2 2 2
22 2222+ + + + += + += + 14. 14. 14. 14. 14. [ ] { } ( ) 8 2 3 38 2
3 38 42 2 2 2 22 2 2 2 22 2x xy y x xy y x xyx xy y x xy y x xyx y+
+ + = + + + += +5.5.5.5.5.( ) 2 3 4 32 3 4 32x y x yx y x yx+ += +
= 10. 10. 10. 10. 10.( ) ( ) + + + = + + = +5 6 5 65 6 5 66 5m mm
mm 15.15.15.15.15. ( ) ( ) ( ) ( ) + + + + += + + +=a b a b b a a
ba b a b b a a b330EJERCICIO 321.1.1.1.1.( ) [ ][ ]2222a a a ba a a
ba a a ba b+ += + = + = 2.2.2.2.2.( ) [ ][ ]3 23 23 24x x y x yx x
y x yx x y x yx + += + = + +=3.3.3.3.3.( ) ( ) [ ][ ]2222 2m mn mnm
mn mnmmn mnm n += = + + += +4.4.4.4.4.( ) ( ) ( )[ ][ ]4 3 2 34 3 2
34 3 2 36 3 42 2 2 2 22 2 2 2 22 2 2 2 22 2x x xy y xy x yx x xy y
xy x yx x xy y xy x yx xy y+ + + += + + + + = + + + = + 5.5.5.5.5.(
) ( ) { }{ }a a b a b c aa a b a b c aa a b a b c aa c+ + + += + +
+ + += + + + += +2226.6.6.6.6.( ) [ ] ( ) [ ][ ] [ ]4 2 3 4 2 14 2
3 4 2 14 2 3 4 2 15 2m m n n mm mn n mm mn n mn + + += + + = + =
+7.7.7.7.7.{ } ( )[ ]( )[ ][ ]2 5 22 5 22 5 22 5 22x x y x yx x y x
yx x y x yx x y x yx y+ + += + += + + + = + + = +8.8.8.8.8.( )[ ] {
}[ ] { }{ }x xy y x xy yx xy y x xy yx xy y x xy yx xy y x xy yx xy
y2 2 2 22 2 2 22 2 2 22 2 2 22 27 3 27 3 27 3 27 3 22 4 3 + + + = +
+ = + = + + + += + +9.9.9.9.9.( ) ( ) { }[ ]{ } [ ][ ] + + + + += +
+ + += + + + + = + + + = a b a b a b a b aa b a b a b a ba b a b a
b a ba b a b a b a ba b3 2 2222210.10.10.10.10.( ) ( ) [ ] { }[ ] {
}{ } + + + += + + + = + + = + + + + += +x y x y x y x yx y x y x y
x yx y x y x y x yx y x y x y x yx y4 24 24 24 2311.11.11.11.11. (
) ( ) ( ) ( ) [ ][ ] + + + + + + = + + + = + + = a b a b a b b a ba
b a b a b b a ba b a b a b b a ba b2 32 32 33 712.12.12.12.12.( ) (
)[ ] { }( )[ ] { }{ }7 3 5 3 2 37 3 5 3 2 37 3 5 3 2 37 3 5 3 2 37
2 52 2 22 2 22 2 22 2 22m m n n m nm m n n m nm m n n m nm m n n m
nm n + + += + + + = + + = + + + + = + 13.13.13.13.13.( ) ( ) ( ) [
] { }[ ] { }{ }2 4 42 4 46 46 4a a b a b a b aa a b a b a b aa b a
b a b aa b a b a b ab + + += + + + = + += + + =14.14.14.14.14.( ) {
} ( )[ ] ( ){ } [ ] ( )[ ] ( )( )3 5 2 63 5 2 63 5 2 63 5 2 63 5 2
65 5 6x y x y x x yx y x y x x yx y x y x x yx y x y x x yx y x y x
x yx y + + + += + + + = + + + = + + = + + + += +15.15.15.15.15. ( )
( ) ( ) { }[ ]{ } [ ][ ]6 2 2 26 2 2 26 2 2 26 2 2 26 7c a c a c a
a c cc a c a c a a c cc a c a c a a c cc a c a c a a c ca c + + + +
+= + += += + + + + + + + = +16.16.16.16.16.( ) ( ) ( ) { }( )[ ]( )
{ } [ ]{ } [ ][ ] + + + += + + + = + + + = + + = + + + += + +3 2 2
2 5 63 2 2 2 5 63 2 2 2 5 63 2 2 2 5 63 2 2 2 5 66 2 1mn m m m n
nmn m m m n nmn m m m n nmn mm m n nmn mm m n nm n17. 17. 17. 17.
17.( ) ( ) ( )[ ]( ){ }( ) [ ] { }[ ] { }{ }2 5 3 2 42 5 3 2 42 5 3
2 42 5 3 2 42 5 3 2 45 6a b a c a b c a ba b a c a b c a ba b a c a
b c a ba b a c a b c a ba b a c a b c a ba b+ + + + + += + + + + +
= + + + + + + + = + + + + = + + + = 18. 18. 18. 18. 18.( ) ( )[ ](
) ( ) ( ) { }( ) [ ] { }[ ] + + + + + += + + + + = + + = + + = 3 2
3 2 3 23 2 3 2 3 23 2 3 2 3 23 2 3 4 2 14x x y x y x x yx x y x y x
x yx x y x y x x yx x y x y19.19.19.19.19.( ) [ ] ( ) [ ] [ ] ( ) [
] { }[ ][ ] [ ] { }{ } + + + + = + = + + += +=a a b c ca a b c ca a
b c cb c cb20.20.20.20.20.( ) [ ] { }( ) [ ] { }( )[ ] { } [ ] { }{
} { } + + += + + = + + = = a b b a a ba b b a a ba b b a a ba b b a
a ba b 3 321.21.21.21.21. ( ) [ ] { } ( ) [ ] { } ( ) { } [ ][ ] {
} [ ] { } { } [ ]{ } { } [ ] + + + + + = + + + + = + + + += + + + +
+= + +a b c c a b a ba b c c a b a ba b c c a b a ba b c c a b a ba
b c 222.22.22.22.22.( ) ( ) { }( ) ( ) { }[ ]( ) { } { }[ ]{ } [ ][
] + + + + + += + + += + + + += + + += + + + + + = + 3 4 2 33 4 2 33
4 2 33 4 2 33 4 2 32 4 7m m n m mn nm m n m mn nm mn m mn nmmn m mn
nmmn m mn nm n23.23.23.23.23. ( ) ( ) ( ) [ ] { } [ ][ ] { }[ ]{ }
[ ][ ] + + + + = + + + = + + + + = += + + = x x y x y z x y yx x y
x y z x y yx x y x y z x y yx x y zx x y z y z22 224.24.24.24.24.(
) ( ) ( ) [ ] { } [ ][ ] { } [ ]{ } [ ][ ] + + + += + + + += + = =
+ +a a a b a b c a ba a a b a b c a ba a c a ba a c a b a b c
3EJERCICIO 331.1.1.1.1. ( )a b c da b c d + = + + 2.2.2.2.2. ( )x
xy yx xy y2 22 23 63 6 += + +3.3.3.3.3. ( )x x xx x x3 23 24 3 14 3
1+ += + +4.4.4.4.4. ( )a a b ab ba a b ab b3 2 2 33 2 2 35 35 3 + =
+ + 5.5.5.5.5. ( )x x x xx x x x4 3 24 3 22 2 12 2 1 + += +
+6.6.6.6.6. ( )22a b c da b c d+ += + 7.7.7.7.7. ( )x x xx x x3 23
23 43 4+ + = +8.8.8.8.8. ( )x x y xy yx x y xy y3 2 2 33 2 2 35 35
3 + = +9.9.9.9.9. ( )a x xy ya x xy y2 2 22 2 222 = +
+10.10.10.10.10. ( )a b bc ca b bc c2 2 22 2 222+ = + +EJERCICIO
341.1.1.1.1.( )( )[ ]x y x yx y x y+ + = 222.2.2.2.2. ( ) ( )( ) (
)[ ]4 2 3 24 2 3 2m n mn mnm n mn mn + + + = + + 3.3.3.3.3.( )[ ](
)[ ] { }x xy x xy yx xy x xy y2 2 22 2 233 + += +4.4.4.4.4. [ ] (
)[ ] ( )[ ]x x x x xx x x x x3 23 23 4 2 3 2 33 4 2 3 2 3 + + += +
+ + +5.5.5.5.5.( )[ ] { }( )[ ] { } [ ]2 3 22 3 2a b a a b aa b a a
b a+ + + = + + + EJERCICIO 356. 6. 6. 6. 6. ( )( )[ ] + += +2 32 3a
a ba a b7.7.7.7.7.( ) ( )( ) ( )[ ]2 32 32 2 2 22 2 2 2x xy y xy x
yx xy y xy x y+ + + += + + +8.8.8.8.8.x x xx x x3 23 23 4 23 4 2 +
= + + { }9. 9. 9. 9. 9. ( )[ ]( )( )[ ]( ){ }m m m mm m m m4 24 23
2 3 2 33 2 3 2 3 + + + += + + +1.1.1.1.1.2 3 6 = 2.2.2.2.2. = 4 8
323.3.3.3.3. = 15 16 2404.4.4.4.4.ab ab a b a b = =+ + 1 1 1 1 2
25.5.5.5.5.2 3 6 62 2 1 3x x x x = =+6.6.6.6.6. = =+ +4 4 42 2 2 1
1 2 3 3a b ab a b a b7.7.7.7.7. = =+ +5 5 53 2 3 1 1 2 4 3x y xy x
y x y8.8.8.8.8.a b a x a b x a b x2 3 2 2 2 3 4 33 3 3 =
=+9.9.9.9.9. = =+4 5 20 202 2 2 1 2 3 2m mn p m n p m n
p10.10.10.10.10.5 6 302 2 2 2a y x a x y = 11.11.11.11.11. = =+x y
y z x y z x y z2 3 3 4 2 3 3 4 2 6 44 4 412.12.12.12.12.abc cd abc
d abc d = =+ 1 1 213.13.13.13.13. = =+15 16 240 2404 3 2 3 2 4 3 3
2 7 3x y a x a x y a x y14.14.14.14.14.3 4 122 3 2 2 3 2a b x y a b
x y = 15.15.15.15.15.3 7 21 212 3 5 2 1 3 1 5 2 4 6a bx b x a b x a
b x = =+ +16.16.16.16.16. = =+8 9 72 722 3 2 4 2 2 1 3 4 2 3 3 4m n
a mx a m n x a m n x17.17.17.17.17.a b ab a bmn m n =+ + 1
118.18.18.18.18. =+ +5 6 302 3 2 3a b a b x a b xmn m
n19.19.19.19.19.x y c x y c x y c x ycmn mn x mmn n x m n x = = + +
+ + 1 2 2 120.20.20.20.20. =+ +m n m n m nx a x a6 62 2 1EJERCICIO
361.1.1.1.1.a a a am m mm m = =+ + + + 1 1 2 12.2.2.2.2. = =+ + +
+x x x xa a a a a 2 2 2 23.3.3.3.3.4 4 41 1 1 1 2 1a b ab a b a bn
x x n x x n x = = + + + + + +4.4.4.4.4. = = + + + + + + + + + +a b
a b a b a bn n n n n n n n n n 1 2 2 1 2 2 2 3 2 25.5.5.5.5. =+ + +
+ + +3 4 124 1 2 3 2 6 2 4a b a b a bn n n n n n6.6.6.6.6.3 4 12
122 3 1 2 2 1 3 2 3 5x y x y x y x ym m m m m m = =+ + + + + + +
+7.7.7.7.7.4 5 202 4 5 1 2 7 2 5x b x b x ba a a a a a + + + + + +
=8.8.8.8.8.a b c a b a b c a bcmn m n mmn n m n = =+ + 2 2 2
39.9.9.9.9. =+ + x y x y c x y cm a m a m a 1 2 3 5 2 2 2 2 3 24
410. 10. 10. 10. 10. = 5 7 351 2 3 4 3 3 2 5m n c m n m n ca b a b
a bEJERCICIO 371.1.1.1.1. 12451245410252 3 5 5 5a a b a b a b a b =
= =2.2.2.2.2. = = =377143771421983142 2 32 5 2 5 2 5m n a ma m n a
m n a m n3.3.3.3.3. 2335615252 3 2 4 2 6 4 2 6 4x y a x y a x y a x
y = = 4.4.4.4.4. = =18454401103 4 3 2 3 5 5 3 5 5m n a m n a m n a
m n5.5.5.5.5. = = 78271456143 4 4abc a a bc a bc6.6.6.6.6. =
=355636123 4 2 5 2 3 9 2 3 9x y a by a bx y a bx y7.7.7.7.7.
1335315151 1a a a am m m = =+ +EJERCICIO 388.8.8.8.8. = =+
+342532153103 1 3 1 3a ab a b a bm m m9.9.9.9.9. 5631012121421 2 1
2a b ab ca b c a b cmnm n m n = = + + + +10.10.10.10.10. = =+ +
+293523152151 12 1 2 1 2 1 2 1a b a ba b a bx m x mx m x
m11.11.11.11.11. 384512403102 3 2 3 2a b a b a b a bmn mn m n m n =
= 12.12.12.12.12. = =+ 211447247871 3 2 3 22 2 1 2 2 2 1 2a b c a
ba b c a b cx x xx x x x1.1.1.1.1.a a a a a = =+ +3 3 32 1 1 2
42.2.2.2.2.3 3 32 3 2 2 2 3 1 2 6x x y a x a x y a x y = =+
+3.3.3.3.3. = =+ + +m n m mn m n m n2 2 3 2 2 1 1 3 5 43 5 15
154.4.4.4.4.4 5 20 202 3 2 2 2 3 1 2 2 6 2 2a a x ay a x y a x y =
=+ +5.5.5.5.5. = = + + + + +a ab a b a b a bm x m x m x2 3 6 62 1 2
1 3 16.6.6.6.6. 122335630153 2 4 2 4 3 1 6 4x a x a m a x m a x m =
=+ +7.7.7.7.7. 233431812322 4 4 12 4 4 1 6 5a a b a ba b a bm xm x
m x = = ++ + + + + +EJERCICIO 398.8.8.8.8. = = + + + +
+35511015503103 22 3 1 2 4m a m a ma m a mx ax a x a9.9.9.9.9.2 3 4
24 242 3 1 2 3 1 7a a a a a a = =+ + +10.10.10.10.10. = = + + + +3
4 560 602 3 23 1 2 2 1 1 6 4b a b ab a xa b x a b x11.11.11.11.11.
a b a ab a xa b x a b xm xm x m x = = + + + + + +2 22 1 2 1 5 12 36
612.12.12.12.12. = =+ + + + +12351033468342 2 3 22 1 3 2 1 2 1 8 4x
y xy x x yx y x y1.1.1.1.1.326 23 24 3x xxx x +2. 2. 2. 2. 2.8 3216
62 235 3 2x y yaxax y ax y3. 3. 3. 3. 3.x xxx x x23 24 322 8 6 + +
4. 4. 4. 4. 4. a a aaba b a b a b3 24 3 24 633 12 18 + +5. 5. 5. 5.
5.a ab baba b a b ab2 23 2 2 322 + + 6. 6. 6. 6. 6. x x xa xa x a x
a x5 32 22 7 2 5 2 36 833 18 24 7. 7. 7. 7. 7.m m n nm xm x m n x m
n x4 2 2 437 5 2 3 43 744 12 28 + + 8. 8. 8. 8. 8. x x y xyax yax y
ax y ax y3 2 236 5 2 4 34 64 6 + +9. 9. 9. 9. 9.a a b aba ma m a bm
a b m3 2 24 27 2 6 2 5 2 25 844 20 32 + +10. 10. 10. 10. 10.a a aaa
a aa a am m mm m mm m m + + = + + + ++ 1 21 1 1 2 11 122 2 22 2
211.11.11.11.11. x x xxx x xm m mmm m m+ + + + 1 123 1 3 3 1333 9
312.12.12.12.12. a b a b a ba ba b a b a bm n m n m nm n m n mn+ +
+ ++ + + + +1 1 2 222 1 1 2 333 3 3EJERCICIO 4013.13.13.13.13. x x
xxx x x x3 225 4 3 23 5 644 12 20 24 + + +14. 14. 14. 14. 14. a a x
a xbxa bx a bx a bx bx4 3 2 234 3 3 4 2 5 36 9 833 18 27 24 + + 15.
15. 15. 15. 15.a a a aa xa x a x a x a xn n n nnn n n n+ + ++ + + +
+ +3 2 122 3 2 2 2 2 2 1 2 2 23 43 416.16.16.16.16. x x x xa xa x a
x a x a x a x4 3 22 32 7 2 6 2 5 2 4 2 36 8 7 533 18 24 21 15 + + +
+ 17.17.17.17.17. + + 3 5 7 4515 25 35 203 2 2 32 22 4 2 2 3 3 2 2
4 2 5x x y xy ya xya x y a x y a x y a xy18.18.18.18.18. x x x xxx
x x xa a a aa a a a+ + + ++ + + + + + +5 4 3 127 6 5 33 522 6 2
1019.19.19.19.19.a a b a b a b ba ya y a b y a b y a b y a b y8 6 2
4 4 2 6 83 211 2 9 2 2 7 4 2 5 6 2 3 8 23 355 15 5 15 5 + + + +
20.20.20.20.20.a b a b a b a ba ba b a b a b a bm n m n m n m nmm n
m n m n m n+ ++ + + + ++ + + +344 12 4 41 2 2 4 3 632 3 2 1 5 2 2 7
2 3 91.1.1.1.1. 1223252104151541521 2 23 2a baa a ba a b=
+2.2.2.2.2.23342349612491233 1 3 1 14 3 2a ba ba b a ba b a b += ++
+3. 3. 3. 3. 3. 35162553151551810155182321 1 2 2 2 12 2 2 3a b caca
c abc aca c abc ac + + = + + + 4. 4. 4. 4. 4.251329365336965232 222
2 2 1 2 24 3 2 2a ab ba xa x a bx a b xa x a bx a b x+ + = + +
+5.5.5.5.5. 1325143236610381235382 232 3 3 1 2 32 3 4 5x xy yyx y
xy yx y xy y = + +6.6.6.6.6.3 5 63109101510181091032952 32 1 3 2 3
2 33 3 2 3 2 3a b ca xa x a bx a cxa x a bx a cx + + = +
+7.7.7.7.7. 2913376633732122137174 2 2 43 44 3 4 2 3 2 4 3 4 47 4 5
6 3 8x x y yx yx y x y x yx y x y x y + += ++ + + +EJERCICIO
418.8.8.8.8. 1213141558516524532540516524532182 2 2 222 2 2 2 2 2 2
24 2 2 2 2 2 2a b x ya ma m a b m a mx a mya m a b m a mx a my + +
+= + ++9.9.9.9.9. 23125619346123815243361238581123 2 2 32 33 2 3 2
2 1 3 1 2 2 3 2 3 35 3 4 4 3 5 2 6m m n mn nm nm n m n m n m nm n m
n m n m n+ + = + + + + + + +10.10.10.10.10.
251335110571035521153557027521371146 4 2 2 4 63 4 33 6 4 3 3 4 4 2
3 3 2 4 4 3 3 4 6 33 10 3 3 8 5 3 6 7 3 4 9x x y x y ya x ya x y a
x y a x y a x ya xy a x y a x y a x y + + += + ++ + + + +
+1.1.1.1.1. aaa aaa a++ + 31332 3223.3.3.3.3. xxx xxx x++ + 5454
2020225.5.5.5.5. + + + +xxx xxx x3535 158 15227.7.7.7.7. 3 226 43
26 2222 2x yx yx xyxy yx xy y++ 2.2.2.2.2. aaa aaa a+ 31332
3224.4.4.4.4.mmm mmm m + +6565 3011 30226.6.6.6.6. ++ ++ +aaa aaa
a2323 65 6228.8.8.8.8.5 43 215 1210 815 22 8222 2x yx yx xyxy yx xy
y + ++ + 9.9.9.9.9. 5 735 715 215 8 21222 2a ba ba abab ba ab b++ +
11.11.11.11.11. + ++ + a ba ba abab ba ab b8 48 84 48 12 4222
213.13.13.13.13. ++ + + + +9 86 454 4836 3254 12 32222 2m nm nm
mnmn nm mn n10.10.10.10.10.7 32 414 628 1214 22 1222xxx xxx x++ +
12.12.12.12.12. 6 56 56 56 11 5222 2m nmnm mnmn nm mn n +
+14.14.14.14.14. + + + +7 32 1114 677 3314 71 3322yyy yyy
yEJERCICIO 421.1.1.1.1. x xy yx yx x y xyx y xy yx y2 23 2 22 2 33
3+ ++ + 5.5.5.5.5. a a aaa a aa a aa a a3 24 3 23 24 212+ + + +9.
9. 9. 9. 9. m m mamaam am am amam am am aam am a3 24 3 23 242222 +
+ + + + 2.2.2.2.2.a ab ba ba a b aba b ab ba a b ab b2 23 2 22 2 33
2 2 32223 3 + + + + 6.6.6.6.6. m m n nm nm m n m nm n m n nm n4 2 2
42 26 4 2 2 44 2 2 4 66 6+ ++ + 10. 10. 10. 10. 10. 3 5 24 512 20
815 25 1012 35 33 102 23 2 22 2 33 2 2 3a ab ba ba a b aba b ab ba
a b ab b + + + + 3.3.3.3.3.a ab ba ba a b aba b ab ba a b ab b2 23
2 22 2 33 2 2 32223 3+ +++ ++ + ++ + +7.7.7.7.7. x x xxx x x xx x
xx x x3 24 3 23 24 32 3 12 32 4 6 23 6 9 32 7 3 + + + + + +
11.11.11.11.11.5 3315 9 35 315 5 9 3 34 2 2 45 3 2 44 2 3 55 4 3 2
2 3 4 5m m n nmnm m n mnm n m n nm m n m n m n mn n + + + + +
4.4.4.4.4.x xxx x xx xx x x3 24 33 24 23 1333 9 39 3 ++ ++ + +
+9.9.9.9.9.3 6 523 6 56 12 103 5 12 10325 3 235 2y yyy y yy yy y y
++ ++ ++ + 12. 12. 12. 12. 12.a aa aa a aa a aa aa a a224 3 23 224
21112 1+ + + + 13.13.13.13.13. x x xx xx x xx x xx x xx x x3 225 4
34 3 23 25 222 522 4 25 10 512 5+ ++ ++ + + 19.19.19.19.19. x xy yx
xy yx x y x yx y x y xyx y xy yx x y xy y2 22 24 3 2 23 2 2 32 2 3
44 3 3 423223 6 33 5 3 + + + + + ++ + + +14.14.14.14.14. m m n mnm
mn nm m n m nm n m n m nm n m n mnm m n m n mn3 2 22 25 4 3 24 3 2
2 33 2 2 3 45 4 2 3 43 22 83 22 6 48 24 165 20 16 + + + + +
20.20.20.20.20. n nnn n nn nn n n224 3 224 32 1122 12 2 1 + + + +
15.15.15.15.15.x xx xx x xx x xx xx x x224 3 23 224 21112 1+ + + +
21.21.21.21.21. a a b aba b ab ba b a b a ba b a b a ba b a b aba b
a b a b ab3 2 22 2 35 4 2 3 34 2 3 3 2 43 3 2 4 55 4 2 2 4 53 42
103 42 6 810 30 405 22 40 + + + + + 16.16.16.16.16. x xx xx x xx x
xx xx x x x x4 226 4 25 34 26 5 3 23 22 33 22 6 43 9 62 6 7 4 6 + +
+ + + + + +22. 22. 22. 22. 22. 8 12 6 92 316 24 12 1824 36 18 2716
24 273 2 2 34 3 2 2 33 2 2 3 44 2 2 4x x y xy yx yx x y x y xyx y x
y xy yx x y y + + + + + 17.17.17.17.17.m m mmm m m mm m mm m m m m3
236 5 4 33 26 5 4 24 1144 14 4 1+ ++ + + + + 23.23.23.23.23. 2 3 42
54 6 2 810 15 5 204 4 13 3 203 24 3 23 24 3 2y y yyy y y yy y yy y
y y + + + + + + 18.18.18.18.18. a aa aa a aa a aa aa a a a325 3 24
235 4 25 255 25 25 25 107 27 10 + + + + + + + +24.24.24.24.24. + +
+ ++ + + + a ax xa ax xa a x a xa x a x axa x ax xa a x a x ax x3 2
32 25 3 2 2 34 2 3 43 2 4 55 4 3 2 4 52 32 32 4 63 6 92 32 3 5 11
325.25.25.25.25.x x y x y xyx xy yx x y x y x yx y x y x y x yx y x
y x y xyx x y x y xy4 3 2 2 32 26 5 4 2 2 35 4 2 3 3 2 44 2 3 3 2 4
56 5 2 4 53 23 23 23 22 3 + + + + + + 30.30.30.30.30. y yy yy y yy
y yy yy y y y y24 26 5 44 3 226 5 4 32 12 222 4 22 4 22 4 4 2 + + +
+ + + + +26.26.26.26.26.a a aa aa a a aa a a aa a aa a a a3 236 5 4
34 3 23 26 5 25 2 32 75 2 32 10 4 67 35 14 215 31 8 21 + + + + + +
+ +31.31.31.31.31. m mm mm m mm m mm mm m m m m m4 237 5 35 34 27 5
4 3 23 43 2 13 9 122 6 83 43 11 18 3 8 4 + + + + + + + +
+27.27.27.27.27. m m mm mm m m mm m m mm m mm m m m4 3 226 5 4 25 4
34 3 26 5 332 332 2 2 63 3 3 95 6 9+ + ++ + + + + + +
+32.32.32.32.32. a a aa a aa a a aa a a aa a a aa a aa a a a a a3
23 26 5 4 35 4 3 24 3 23 26 5 4 3 212 12 2 2 212 2 3 2 1+ ++ + ++ +
+ + + + + 28.28.28.28.28.a a b a b ab ba ab ba a b a b a b a ba b a
b a b a b aba b a b a b ab ba a b a b a b ab b4 3 2 2 3 42 26 5 4 2
3 3 2 45 4 2 3 3 2 4 54 2 3 3 2 4 5 66 5 4 2 3 3 5 63232 2 6 2 234
6 3+ + ++ + + + + + + + +33. 33. 33. 33. 33. 8 12 63 2 424 36 18
316 24 12 232 48 24 424 52 38 33 26 43 2 2 32 25 4 3 2 2 34 3 2 2 3
43 2 2 3 4 55 4 3 2 2 3 4 5x x y xy yx xy yx x y x y x yx y x y x y
xyx y x y xy yx x y x y x y xy y + + + + + + + + +29.29.29.29.29.x
x y x y xy yx xy yx x y x y x y x yx y x y x y x y xyx y x y x y xy
yx x y x y x y xy y4 3 2 2 3 42 26 5 4 2 3 3 2 45 4 2 3 3 2 4 54 2
3 3 2 4 5 66 4 2 3 3 2 4 5 622 2 2 2 22 2 2 3 2 + ++ + ++ + + + + +
+ 34.34.34.34.34.5 4 2 3 12 25 4 2 310 8 4 6 210 8 4 6 25 4 8 5 5 2
6 6 24 3 24 28 7 6 5 46 5 4 3 24 3 28 7 6 5 4 3 2a a a aa aa a a a
aa a a a aa a a aa a a a a a a a + + + + + ++ + + + +
35.35.35.35.35. x x x xx x xx x x x xx x x x xx x x x xx x x xx x x
x x4 3 23 27 6 5 4 36 5 4 3 25 4 3 24 3 27 6 5 212 3 62 2 2 2 23 3
3 3 36 6 6 6 63 6 3 6 + + + + + + + + + + ++ + + + + +40. 40. 40.
40. 40.3 6 2 3 23 4 53 6 2 3 29 18 6 9 612 24 8 12 815 30 10 15 103
15 14 28 47 28 23 105 3 24 29 7 6 5 47 5 4 3 26 4 3 25 3 29 7 6 4 3
2a a a aa a aa a a a aa a a a aa a a a aa a a aa a a a a a a + + +
+ + + + + + + + + + + + 36.36.36.36.36. 3 2 5 42 13 2 5 43 2 5 46 4
10 83 2 5 43 5 9 10 8 3 43 23 26 5 4 35 4 3 24 3 23 26 5 4 3 2a a
aa a aa a a aa a a aa a a aa a aa a a a a a+ + ++ + + + ++ + + + +
41.41.41.41.41.a b ca b ca ab acab b bcac bc ca b bc c+ ++ ++ + +
2222 2 2237.37.37.37.37.5 3 4 23 15 3 4 215 9 12 65 3 4 25 3 11 11
17 3 4 24 3 24 28 7 6 56 5 4 34 3 28 7 6 5 4 3 2y y y yy yy y y yy
y y yy y y yy y y y y y y y + + + + + + + 42. 42. 42. 42. 42. x y
zx y zx xy xzxy y yzxz yz zx xy y yz z+ ++ ++ + + + 22222 32222 2
238. 38. 38. 38. 38.m m n m n nm m n mn nm m n m n m nm n m n m n m
nm n m n m n mnm n m n m n nm m n m n m n m n m n mn n4 3 2 2 43 2
2 37 6 5 2 3 46 5 2 4 3 2 55 2 4 3 3 4 64 3 3 4 2 5 77 6 5 2 4 3 3
4 2 5 6 72 3 43 52 3 43 6 9 125 10 15 202 3 45 14 20 13 9 20 4 + +
+ + ++ + + ++ + + + + 43.43.43.43.43.2 3 522 3 52 3 54 6 102 5 3
102222 2 2x y zx y zx xy xzxy y yzxz yz zx xy xz y yz z + + + + +
++ + + +39.39.39.39.39.x x y x y yx x y xyx x y x y x yx y x y x y
x yx y x y x y xyx x y x y x y x y xy6 4 2 2 4 65 3 2 411 9 2 7 4 5
69 2 7 4 5 6 3 87 4 5 6 3 8 1011 9 2 7 4 5 6 3 8 1032 332 6 2 23 9
3 35 8 6 5 3 + + + + + + + + + 44.44.44.44.44.x xy xz y yz zx y zx
x y x z xy xyz xzx y xy xyz y y z yzx z xyz xz y z yz zx xyz y z2 2
23 2 2 2 22 2 3 2 22 2 2 2 33 3 33 + ++ + + ++ + ++ + + +
+EJERCICIO 431.1.1.1.1.a a aaa a aa a aa ax x xx x xx x xx x+ ++ +
++ ++ ++ ++ ++2 13 2 12 1312.2.2.2.2. + ++ + + + + + + ++ + ++ + ++
+ ++ + + +x x xx xx x xx x xx x x xn n nn n nn n nn n n n3 2 125 4
34 3 25 4 3 22223 3.3.3.3.3. m m m mm mm m m mm m m mm m m mm m m m
ma a a aa a a aa a a aa a a aa a a a a+ + + + + ++ + ++ + + + + + +
++ + + + + + + +2 1 124 3 2 13 2 12 1 14 3 1 12 32 2 2 23 3 3 36 5
34.4.4.4.4. a a aa aa a aa a aa a a an n nn nn n nn n nn n n n+ +++
+ ++ ++ + ++ ++ + + + + 2 112 3 2 2 2 12 2 2 1 22 3 2 2 2 1 23 23
23 24 25.5.5.5.5.x x xx xx x xx x xx x x x xa a aa aa a aa a aa a a
a a+ ++ ++ + ++ + ++ + + + ++ + ++ +2 13 12 5 2 4 2 32 3 2 2 2 12 5
2 4 2 3 2 2 2 12222 4 22 3 4 26.6.6.6.6.a a aa aa a aa a aa a aa a
a ax x xx x xx x xx x xx x x x ++ ++ + + + + ++ + 2 32 12 32 4 62
32 8 31 222 11 11 22 1 27.7.7.7.7. a a aa a aa a aa a aa a aa a a a
ax x xx xxx x xx x xx x xx x x x x+ ++ ++ + + + 3 23 23 23 22 4 5
21 2122 2 1 2 22 1 2 2 2 32 2 2 3 2 42 2 1 2 2 2 3 2 48.8.8.8.8. m
m m mm m mm m m mm m m mm m m mm m m m m ma a a aa aaa a a aa a a
aa a a aa a a a a a+ + + + + + ++ + + + + + + + + + + + ++ + + + +4
3 2 11 232 3 2 2 2 1 22 2 2 1 2 2 12 1 2 2 1 2 22 3 2 2 2 1 2 2 1 2
222222 2 49.9.9.9.9. x x x xx x xx x x xx x x xx x x xx x x xa a a
aa aaa a a aa a a aa a a aa a a a + + + + + + + 1 2 3 41 232 2 2 3
2 4 2 52 3 2 4 2 5 2 62 4 2 5 2 6 2 72 2 2 3 2 4 2
72222410.10.10.10.10. a b a b a b a ba b a bab a b a b a ba b a b a
b a bab a b a b a b a bn n n nn nn n n nn n n nn n n n n + + + + +
+ 1 2 2 3 3 42 2 42 3 2 1 4 2 2 5 2 3 62 2 5 2 3 6 2 4 7 2 5 82 3 2
1 4 2 2 5 2 4 7 2 5 8222211.11.11.11.11.a ba ba a ba b ba a b a b
bx xm mmx m xx m mxmx m x x m mx++++ ++ + ++++ +12.12.12.12.12.a ba
ba aba b ba ab a b bx nx nx nx n x n + +1 1111 113. 13. 13. 13. 13.
+ + + + ++ + + + + ++ + + + 5 36 830 6 1840 8 245 330 46 5 23 32 2
2 1 23 1 3 2 3 35 1 5 5 15 5 1 5 25 1 5 2 5 35 1 5 5 1 5 2 5 3a a
aa a aa a aa a aa a aa a a a am m mm m mm m mm m mm m mm m m m
m14.14.14.14.14. x y x y x yx y x y x yx y x y x yx y x y x yx y x
y x yx y x y xa x a x a xa x a x a xa x a x a xa x a x a xa x a x a
xa x a x+ + + + ++ + + + + + +2 1 1 12 1 2 2 2 1 2 33 1 2 3 3 2 2 3
1 2 13 2 2 3 1 2 1 3 2 23 1 2 1 3 2 2 3 3 2 13 1 2 3 3 2 2 34 32 4
102 8 64 16 1210 40 302 4 28a x a xy x y +2 2 3 3 2 130EJERCICIO
441.1.1.1.1. 1213131216191416164 936161653616222 22 2a ba ba abab
ba ab ba ab b++ = + 2.2.2.2.2. x yx yx xyxy yx xy yx xy yx xy y++ =
+ = + 25135613215561030134 25301030132130131371013222 22 22
23.3.3.3.3. 12131423322629212343638268 27362
612381335368123813353623382 23 2 22 2 33 2 2 33 2 2 33 2 2 3x xy yx
yx x y xyx y xy yx x y xy yx x y xy yx x y xy y + + + +++= + = +
4.4.4.4.4. 14231432116142123832661162 382 181211658201211658532 23
2 22 2 33 2 2 33 2 2 33 2 2a ab ba ba a b aba b ab ba a b ab ba a b
ab ba a b ab b + + + +++= + = + 5.
251312322610363425131245232261015 123045 20 48603
4622610330176076351101760762 22 24 3 2 23 2 2 32 2 3 44 3 2 2 3 44
3 2 2 3 44 3 2 2 3 4m mn nm mn nm m n m nm n m n mnm n mn nm m n m
n mn nm m n m n mn nm m n m n mn n+ ++ ++ + ++ ++= + + = + + 7. + +
+ + ++ + + +++ += + + += + + +1213323223343694121332262966343 3627
4 41227 418663466191223186634191223182 22 24 3 2 23 2 2 32 2 3 44 3
2 2 3 44 3 2 2 3 44 3 2 2 3 4x ax ax ax ax ax a xax a x a xa x a x
ax ax a x a x ax ax a x a x ax ax a x a x a9.
141314123211015383638341401301401201201151201103860 312045 4 612090
3 81201 1201103863120471207912022011038214047120791201101103 225 4
3 24 3 23 25 4 3 25 4 3 2 5 4 3 2x x xx xx x x xx x x xx x xx x x x
xx x x x x x x x x x+ ++ + ++ + + + ++ ++ ++= + + + = + + + 6.
3814252132682445324112215682445682496 151202 18248
306045341211112016243860453412374023193045235 4 33 225 4 3 25 4 3
25 4 3 2x xx xx x xx x xx xx x x x xx x x x xx x x x x+ ++ ++ + +
+++= + + + = + + + 8. 2715121423562281201842121526104253051222821
80420105 112 20084010
5305122281014204178401530512114101420139280123 2 22 25 4 3 24 3 2 2
33 2 2 3 45 4 3 2 2 3 45 4 3 2 2 3 45 4 3 2 2 3x x y xyx xy yx x y
x yx y x y x yx y x y xyx x y x y x y xyx x y x y x y xyx x y x y x
y + + + + + ++++ +++= + += + +5124xy10. 10. 10. 10.
10.341225142323526122641521261226415212158541010586124 61232 40
22512010 16 756020 12012058121012297120101603 2 2 32 25 4 3 2 2 34
3 2 2 3 43 2 2 3 4 55 4 3 2 2 3 4 55 4 3 2 2 3m m n mn nm mn nm m n
m n m nm n m n m n mnm n m n mn nm m n m n m n mn nm m n m n m n +
+ + + ++ + +++ ++ +++= + + 14012058125699401016076584 5 5 4 3 2 2 3
4 5mn n m m n m n m n mn n = + + EJ ERCI CI O 451.1.1.1.1. x x x
por xx x x x3 2 25 4 211 1 11 0 11 1 11 1 11 1 0 1 1 + ++ + + + + =
+ 2.2.2.2.2.x x x por x xx x x x x x4 3 2 3 27 6 5 4 3 23 5 8 2 71
3 5 0 81 2 0 71 3 5 0 82 6 10 0 167 21 35 0 561 1 11 3 13 19 0 5611
3 13 19 56+ + + + + + + + + + + + + + + + + = + + + 3.3.3.3.3. a a
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