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CAPITULO XXVIII

Problemas sobre ecuaciones simultaneas
Ejercicio 207
Desarrollar:
  1. (2a+3b ) 3 =8 a 3 +3(4 a 2 ) (3b ) +3(2a ) (9 b 2 ) +27 b 3 =8 a 3 +36 a 2 b+54a b 2 +27 b 3
  2. (4a3 b 2 ) 3 =64 a 3 3(16 a 2 ) (3 b 2 ) +3(4a ) (9 b 4 ) 27 b 6 =64 a 3 144 a 2 b 2 +108a b 4 27 b 6
  3. (5 x 2 +6 y 3 ) 3 =125 x 6 +3(25 x 4 ) (6 y 3 ) +3(5 x 2 ) (36 y 6 ) +216 y 9 =125 x 6 +450 x 4 y 3 +540 x 2 y 6 +216 y 9
  4. (4 x 3 3x y 2 ) 3 =64 x 9 3(16 x 6 ) (3x y 2 ) +3(4 x 3 ) (9 x 2 y 4 ) 27 x 3 y 6 =64 x 9 144 x 7 y 2 +108 x 5 y 4 27 x 3 y 6
  5. (7 a 4 5 a 2 b 3 ) 3 =343 a 12 3(49 a 8 ) (5 a 2 b 3 ) +3(7 a 4 ) (25 a 4 b 6 ) 125 a 6 b 9 =343 a 12 735 a 10 b 3 +525 a 8 b 6 125 a 6 b 9
  6. ( a 8 +9 a 5 x 4 ) 3 = a 24 +3( a 16 ) (9 a 5 x 4 ) +3( a 8 ) (81 a 10 x 8 ) +729 a 15 x 12 = a 24 +27 a 21 x 4 +243 a 18 x 8 +729 a 15 x 12
  7. (8 x 4 7 x 2 y 4 ) 3 =512 x 12 3(64 x 8 ) (7 x 2 y 4 ) +3(8 x 4 ) (49 x 4 y 8 ) 343 x 6 y 12 =512 x 12 1344 x 10 y 4 +1176 x 8 y 8 343 x 6 y 12
  8. (3 a 2 b5 a 3 b 2 ) 3 =27 a 6 b 3 3(9 a 4 b 2 ) (5 a 3 b 2 ) +3(3 a 2 b ) (25 a 6 b 4 ) 125 a 9 b 6 =27 a 6 b 3 135 a 7 b 4 +225 a 8 b 5 125 a 9 b 6
  9. ( 1 2 a+ 2 3 b 2 ) 3 = a 3 8 + 3 ( a 2 ) ( 2 b 2 3 ) + 3 ( a 2 ) ( b 4 ) + 8 b 6 27 = a 3 8 + a 2 b 2 2 + 2a b 4 3 + 8 b 6 27
  10. ( 3 4 a 2 4 5 b 2 ) 3 = 27 a 6 64 3( 9 a 4 ) ( 4 b 2 5 ) +3( 3 a 2 4 ) ( b 4 25 ) 64 b 6 125 = 27 a 6 64 27 a 4 b 2 20 + 36 a 2 b 4 25 64 b 6 125
  11. ( 5 6 a 2 b 3 10 b 4 ) 3 = 125 a 6 b 3 216 3 ( a 4 b 2 ) ( 3 b 4 ) + 3 ( 5 a 2 b ) ( 9 b 8 ) 27 b 12 1000 = 125 a 6 b 3 216 5 a 4 b 6 8 + 9 a 2 b 9 40 27 b 12 1000
  12. ( 7 8 x 5 4 7 y 6 ) 3 = 343 x 15 512 3( x 10 ) ( 4 y 6 7 ) +3( 7 x 5 8 ) ( y 12 ) + 64 y 18 343 = 343 x 15 512 21 x 10 y 6 16 + 6 x 5 y 12 7 + 64 y 18 343
  13. ( x 2y + 3y x 2 ) 3 = x 3 8 y 3 +3( x 2 4 y 2 ) ( 3 y x 2 ) +3( x 2 y ) ( 9 y 2 x ) + 27 y 3 x 6 = x 3 8 y 3 + 9 4y + 27y 2 x 3 + 27 y 3 x 6
  14. ( 2 a 2 5 5 2 b 3 ) 3 = 8 a 6 125 3( a 4 ) ( 5 2 b 3 ) +3( 2 a 2 5 ) ( b 6 ) 125 8 b 9 = 8 a 6 125 6 a 4 5 b 3 + 15 a 2 2 b 6 125 8 b 9
  15. (4 x 4 3x y 3 ) 3 =64 x 12 3(16 x 8 ) ( 3x y 3 ) +3(4 x 4 ) ( 9 x 2 y 6 ) 27 x 3 y 9 =64 x 12 144 x 9 y 3 + 108 x 6 y 6 27 x 3 y 9
  16. ( 3a 2b + 4 b 2 5 ) 3 = 27 a 3 8 b 3 +3( 9 a 2 4 b 2 ) ( 4 b 2 5 ) +3( 3a 2b ) ( b 25 ) + 64 b 6 125 = 27 a 3 8 b 3 + 27 a 2 5 + 72a b 3 25 + 64 b 6 125
  17. ( 7 8 x 4 y 5 ) 3 = 343 512 3( 49 64 ) x 4 y 5 +3( 7 8 ) x 8 y 10 x 12 y 15 = 343 512 147 64 x 4 y 5 + 21 8 x 8 y 10 x 12 y 15
  18. ( 1 6 m 3 6 n 2 m 2 ) 3 = m 9 216 3 ( m ) ( 6 n 2 m 2 ) +3( m 3 6 ) ( n 4 m 4 ) 216 n 6 m 6 = m 9 216 m 4 n 2 2 + 18 n 4 m 216 n 6 m 6