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CAPITULO XXVIII

Problemas sobre ecuaciones simultaneas
Ejercicio 210
Desarrollar:
  1. (x2 ) 4 = x 4 4 x 3 ( 2 ) + 4.3 2 x 2 ( 2 ) 2 6.2 3 x ( 2 ) 3 + 2 4 = x 4 8 x 3 +24 x 2 32x+16
  2. (a+3 ) 4 = a 4 +4 a 3 ( 3 ) + 4.3 2 a 2 ( 3 ) 2 + 6.2 3 a ( 3 ) 3 + 3 4 = a 4 +12 a 3 +54 a 2 +108a+81
  3. (2x ) 5 = 2 5 5 ( 2 ) 4 x+ 5.4 2 ( 2 ) 3 x 2 10.3 3 ( 2 ) 2 x 3 + 10.2 4 ( 2 ) x 4 x 5 =3280x+80 x 2 40 x 3 +10 x 4 x 5
  4. (2x+5y ) 4 = (2x ) 4 +4 (2x ) 3 (5y ) + 4.3 2 (2x ) 2 (5y ) 2 + 6.2 3 (2x ) (5y ) 3 + (5y ) 4 =16 x 4 +160 x 3 y+600 x 2 y 2 +1000x y 3 +625 y 4
  5. (a3 ) 6 = a 6 6 a 5 ( 3 ) + 6.5 2 a 4 ( 3 ) 2 15.4 3 a 3 ( 3 ) 3 + 20.3 4 a 2 ( 3 ) 4 15.2 5 a ( 3 ) 5 + 3 6 = a 6 18 a 5 +135 a 4 540 a 3 +1215 a 2 1458a+729
  6. (2ab ) 6 = (2a ) 6 6 (2a ) 5 ( b ) + 6.5 2 (2a ) 4 ( b ) 2 15.4 3 (2a ) 3 ( b ) 3 + 20.3 4 (2a ) 2 ( b ) 4 15.2 5 2a ( b ) 5 + b 6 =64 a 6 192 a 5 b+240 a 4 b 2 160 a 3 b 3 +60 a 2 b 4 12a b 5 + b 6
  7. ( x 2 +2 y 3 ) 5 = ( x 2 ) 5 +5 ( x 2 ) 4 (2 y 3 ) + 5.4 2 ( x 2 ) 3 (2 y 3 ) 2 + 10.3 3 ( x 2 ) 2 (2 y 3 ) 3 + 10.2 4 ( x 2 ) (2 y 3 ) 4 + (2 y 3 ) 5 = x 10 +10 x 8 y 3 +40 x 6 y 6 +80 x 4 y 9 +80 x 2 y 12 +32 y 15
  8. ( x 3 +1 ) 6 = ( x 3 ) 6 6 ( x 3 ) 5 ( 1 ) + 6.5 2 ( x 3 ) 4 ( 1 ) 2 15.4 3 ( x 3 ) 3 ( 1 ) 3 + 20.3 4 ( x 3 ) 2 ( 1 ) 4 15.2 5 x 3 ( 1 ) 5 + 1 6 = x 18 6 x 15 +15 x 12 20 x 9 +15 x 6 6 x 3 +1
  9. (2a3b ) 5 = (2a ) 5 5 (2a ) 4 (3b ) + 5.4 2 (2a ) 3 (3b ) 2 10.3 3 (2a ) 2 (3b ) 3 + 10.2 4 (2a ) (3b ) 4 (3b ) 5 =32 a 5 240 a 4 b+720 a 3 b 2 1080 a 2 b 3 +810a b 4 243 b 5
  10. ( x 4 5 y 3 ) 6 = ( x 4 ) 6 6 ( x 4 ) 5 (5 y 3 ) + 6.5 2 ( x 4 ) 4 (5 y 3 ) 2 15.4 3 ( x 4 ) 3 (5 y 3 ) 3 + 20.3 4 ( x 4 ) 2 (5 y 3 ) 4 15.2 5 x 4 (5 y 3 ) 5 + (5 y 3 ) 6 = x 24 30 x 20 y 3 +375 x 16 y 6 2500 x 12 y 9 +9375 x 8 y 12 18750 x 4 y 15 +15625 y 18
  11. (2x y 2 ) 6 = (2x ) 6 6 (2x ) 5 ( y 2 ) + 6.5 2 (2x ) 4 ( y 2 ) 2 15.4 3 (2x ) 3 ( y 2 ) 3 + 20.3 4 (2x ) 2 ( y 2 ) 4 15.2 5 2x ( y 2 ) 5 + ( y 2 ) 6 =64 x 6 96 x 5 y+60 x 4 y 2 20 x 3 y 3 + 15 4 x 2 y 4 3 8 x y 5 + y 64 6
  12. (3 x 2 3 ) 5 = ( 3 ) 5 5 ( 3 ) 4 ( x 2 3 ) + 5.4 2 ( 3 ) 3 ( x 2 3 ) 2 10.3 3 ( 3 ) 2 ( x 2 3 ) 3 + 10.2 4 ( 3 ) ( x 2 3 ) 4 ( x 2 3 ) 5 =243135 x 2 +30 x 4 10 3 x 6 + 5 27 x 8 x 10 243
  13. (2 m 3 3 n 4 ) 6 = (2 m 3 ) 6 6 (2 m 3 ) 5 (3 n 4 ) + 6.5 2 (2 m 3 ) 4 (3 n 4 ) 2 15.4 3 (2 m 3 ) 3 (3 n 4 ) 3 + 20.3 4 (2 m 3 ) 2 (3 n 4 ) 4 15.2 5 (2 m 3 ) (3 n 4 ) 5 + (3 n 4 ) 6 =64 m 18 576 m 15 n 4 +2160 m 12 n 8 4320 m 9 n 12 +4860 m 6 n 16 2916 m 3 n 20 +729 n 24
  14. ( x 2 3 ) 7 = ( x 2 ) 7 7 ( x 2 ) 6 ( 3 ) + 7.6 2 ( x 2 ) 5 ( 3 ) 2 21.5 3 ( x 2 ) 4 ( 3 ) 3 + 35.4 4 ( x 2 ) 3 ( 3 ) 4 35.3 5 ( x 2 ) 2 ( 3 ) 5 + 21.2 6 ( x 2 ) ( 3 ) 6 ( 3 ) 7 = x 14 21 x 12 +189 x 10 945 x 8 +2835 x 6 5103 x 4 +5103 x 2 2187
  15. (3a b 2 3 ) 5 = (3a ) 5 5 (3a ) 4 ( b 2 3 ) + 5.4 2 (3a ) 3 ( b 2 3 ) 2 10.3 3 (3a ) 2 ( b 2 3 ) 3 + 10.2 4 (3a ) ( b 2 3 ) 4 ( b 2 3 ) 5 =243 a 5 135 a 4 b 2 +30 a 3 b 4 10 3 a 2 b 6 + 5 27 a b 8 b 10 243
  16. ( x 2 +2 y 2 ) 7 = ( x 2 ) 7 +7 ( x 2 ) 6 (2 y 2 ) + 7.6 2 ( x 2 ) 5 (2 y 2 ) 2 + 21.5 3 ( x 2 ) 4 (2 y 2 ) 3 + 35.4 4 ( x 2 ) 3 (2 y 2 ) 4 + 35.3 5 ( x 2 ) 2 (2 y 2 ) 5 + 21.2 6 ( x 2 ) (2 y 2 ) 6 + (2 y 2 ) 7 = x 14 +14 x 12 y 2 +84 x 10 y 4 +280 x 8 y 6 +560 x 6 y 8 +672 x 4 y 10 +448 x 2 y 12 +128 y 14
  17. ( x 3 1 ) 8 = ( x 3 ) 8 8 ( x 3 ) 7 ( 1 ) + 8.7 2 ( x 3 ) 6 ( 1 ) 2 28.6 3 ( x 3 ) 5 ( 1 ) 3 + 56.5 4 ( x 3 ) 4 ( 1 ) 4 70.4 5 ( x 3 ) 3 ( 1 ) 5 + 56.3 6 ( x 3 ) 2 ( 1 ) 6 28.2 7 ( x 3 ) ( 1 ) 7 + ( 1 ) 8 = x 24 8 x 21 +28 x 18 56 x 15 +70 x 12 56 x 9 +28 x 6 8 x 3 +1
  18. ( x 2 y 2 ) 9 = ( x 2 ) 9 9 ( x 2 ) 8 ( y 2 ) + 9.8 2 ( x 2 ) 7 ( y 2 ) 2 36.7 3 ( x 2 ) 6 ( y 2 ) 3 + 84.6 4 ( x 2 ) 5 ( y 2 ) 4 126.5 5 ( x 2 ) 4 ( y 2 ) 5 + 126.4 6 ( x 2 ) 3 ( y 2 ) 6 84.3 7 ( x 2 ) 2 ( y 2 ) 7 + 36.2 8 ( x 2 ) ( y 2 ) 8 ( y 2 ) 9 = x 18 9 2 x 16 y+9 x 14 y 2 21 2 x 12 y 3 + 63 8 x 10 y 4 63 16 x 8 y 5 + 21 16 x 6 y 6 9 32 x 4 y 7 + 9 256 x 2 y 8 y 9 512
  19. (2 m 3 n 4 ) 7 = (2 m 3 ) 7 7 (2 m 3 ) 6 ( n 4 ) + 7.6 2 (2 m 3 ) 5 ( n 4 ) 2 21.5 3 (2 m 3 ) 4 ( n 4 ) 3 + 35.4 4 (2 m 3 ) 3 ( n 4 ) 4 35.3 5 (2 m 3 ) 2 ( n 4 ) 5 + 21.2 6 (2 m 3 ) ( n 4 ) 6 ( n 4 ) 7 =128 m 21 448 m 18 n 4 +672 m 15 n 8 560 m 12 n 12 +280 m 9 n 16 84 m 6 n 20 +14 m 3 n 24 n 28
  20. ( x 2 2 + 2 y 2 3 ) 5 = ( x 2 2 ) 5 +5 ( x 2 2 ) 4 ( 2 y 2 3 ) + 5.4 2 ( x 2 2 ) 3 ( 2 y 2 3 ) 2 + 10.3 3 ( x 2 2 ) 2 ( 2 y 2 3 ) 3 + 10.2 4 ( x 2 2 ) ( 2 y 2 3 ) 4 + ( 2 y 2 3 ) 5 = x 10 32 + 5 x 8 y 2 24 + 5 x 6 y 4 9 + 20 x 4 y 6 27 + 40 x 2 y 8 81 + 32 y 10 243
  21. ( 1 5 5a 2 ) 6 = ( 1 5 ) 6 6 ( 1 5 ) 5 ( 5a 2 ) + 6.5 2 ( 1 5 ) 4 ( 5a 2 ) 2 15.4 3 ( 1 5 ) 3 ( 5a 2 ) 3 + 20.3 4 ( 1 5 ) 2 ( 5a 2 ) 4 15.2 5 ( 1 5 ) ( 5a 2 ) 5 + ( 5a 2 ) 6 = 1 15625 3a 625 + 3 a 2 20 5 a 3 2 + 375 a 4 16 1875 a 5 16 + 15625 a 6 64