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CAPITULO XXXI

R a d i c a l e s
Resolución de Ecuaciones con radicales que se reducen a primer grado
Ejercicio252
Resolver las ecuaciones:
  1. x + x+5 = 10 x x 2 + x(x+5 ) =10 x+ x(x+5 ) =10 ( x(x+5 ) ) 2 = (10x ) 2 x 2 +5x =10020x+ x 2 5x+20x =100 25x =100 x = 25 x =4
  2. 4x11 +2 x = 55 4x11 (4x11 ) 2 +2 x(4x11 ) =55 4x11+2 x(4x11 ) =55 2 x(4x11 ) =664x 2 x(4x11 ) = 2 (332x ) ( x(4x11 ) ) 2 = (332x ) 2 4 x 2 11x =1089132x+ 4 x 2 132x11x =1089 121x =1089 x = 121 x =9
  3. x x7 = 4 x x 2 x(x7 ) =4 x x 2 7x =4 (x4 ) 2 = ( x 2 7x ) 2 x 2 8x+16 = x 2 7x 8x+7x =16 x =16 x =16
  4. x 2 x +4 = x +1 x +13 ( x 2 ) ( x +13 ) =( x +1 ) ( x +4 ) x 2 +13 x 2 x 26 = x 2 +4 x + x +4 11 x 5 x =26+4 6 x =30 x = 6 (x ) 2 = 5 2 x =25
  5. 6 x+8 = x+8 x 6 = ( x+8 ) 2 x(x+8 ) 6 =x+8 x 2 +8x x 2 +8x =x+86 ( x 2 +8x ) 2 = (x+2 ) 2 x 2 +8x = x 2 +4x+4 8x4x =4 4x =4 x = 4 4 x =1
  6. x3 + 8 x+9 = x+9 (x3 ) (x+9 ) +8 x+9 = x+9 x 2 +6x27 +8 = (x+9 ) 2 x 2 +6x27 +8 =x+9 ( x 2 +6x27 ) 2 = (x+1 ) 2 x 2 +6x27 = x 2 +2x+1 6x2x =27+1 4x =28 x = 4 x =7
  7. x +4 x 2 = x +11 x 1 ( x +4 ) ( x 1 ) =( x +11 ) ( x 2 ) x 2 x +4 x 4 = x 2 2 x +11 x 22 3 x =9 x 22+4 6 x =18 x = 6 (x ) 2 = 3 2 x =9
  8. 2 x+6 4x3 = 9 4x3 2 (x+6 ) (4x3 ) (4x3 ) 2 =9 2 4 x 2 3x+24x18 4x+3 =9 2 4 x 2 +21x18 =93+4x 2 ( 4 x 2 +21x18 ) 2 = 2 (2x+3 ) 2 4 x 2 +21x18 = 4 x 2 +12x+9 21x12x =18+9 9x =27 x = 9 x =3
  9. x 2 x +2 = 2 x 5 2 x 1 ( x 2 ) (2 x 1 ) =(2 x 5 ) ( x +2 ) 2 x 2 x 4 x +2 = 2 x 2 +4 x 5 x 10 2+10 =4 x 12 =4 x ( 4 ) 2 = (x ) 2 x =9
  10. x+14 x7 = 6 x7 (x+14 ) (x7 ) (x7 ) 2 =6 x 2 +7x98 x+7 =6 x 2 +7x98 =67+x ( x 2 +7x98 ) 2 = (x1 ) 2 x 2 +7x98 = x 2 2x+1 7x+2x =98+1 9x =99 x = 9 x =11