Ejercicio 269

Comparte esto 👍👍
CAPITULO XXXIII

Ecuaciones de segundo grado por descomposición en factores
Ejercicio 269
Resolver por descomposición en factores:
  1. x 2 x6 =0 (x3 ) (x+2 ) =0 x3 =0 x 1 =3 x+2 =0 x 2 =2
  2. x 2 +7x =18 x 2 +7x18 =0 (x+9 ) (x2 ) =0 x+9 =0 x 1 =9 x2 =0 x 2 =2
  3. 8x65 = x 2 x 2 +8x65 =0 (x+13 ) (x5 ) =0 x+13 =0 x 1 =13 x5 =0 x 2 =5
  4. x 2 =1083x x 2 +3x108 =0 (x+12 ) (x9 ) =0 x+12 =0 x 1 =12 x9 =0 x 2 =9
  5. 2 x 2 +7x4 =0 2 x 2 x+8x4 =0 x(2x1 ) +4(2x1 ) =0 (2x1 ) (x+4 ) =0 x+4 =0 x 1 =4 2x1 =0 2x =1 x 2 = 1 2
  6. 6 x 2 =1011x 6 x 2 +11x10 =0 6 x 2 4x+15x10 =0 2x(3x2 ) +5(3x2 ) =0 (3x2 ) (2x+5 ) =0 3x2 =0 x 1 = 2 3 2x+5 =0 x 2 = 5 2
  7. 20 x 2 27x =14 20 x 2 27x14 =0 20 x 2 35x+8x14 =0 5x(4x7 ) +2(4x7 ) =0 (4x7 ) (5x+2 ) =0 4x7 =0 x 1 = 7 4 5x+2 =0 x 2 = 2 5
  8. 7x =1530 x 2 30 x 2 +7x15 =0 30 x 2 18x+25x15 =0 6x(5x3 ) +5(5x3 ) =0 (5x3 ) (6x+5 ) =0 6x+5 =0 x 1 = 5 6 5x3 =0 x 2 = 3 5
  9. 60 =8 x 2 +157x 8 x 2 +157x60 =0 8 x 2 +160x3x60 =0 8x(x+20 ) 3(x+20 ) =0 (x+20 ) (8x3 ) =0 x+20 =0 x 1 =20 8x3 =0 x 2 = 3 8
  10. x(x1 ) 5(x2 ) =2 x 2 x5x+102 =0 x 2 6x+8 =0 (x4 ) (x2 ) =0 x4 =0 x 1 =4 x2 =0 x 2 =2
  11. (x2 ) 2 (2x+3 ) 2 =80 [(x2 ) +(2x+3 ) ] [(x2 ) (2x+3 ) ] =80 [x2+2x+3 ] [x22x3 ] =80 (3x+1 ) (x5 ) =80 3 x 2 15xx5+80 =0 3 x 2 16x+75 =0 3 x 2 +16x75 =0 3 x 2 9x+25x75 =0 3x(x3 ) +25(x3 ) =0 (x3 ) (3x+25 ) =0 x3 =0 x 1 =3 3x+25 =0 x 2 = 25 3
  12. 6 x 2 9 x = 4 3 69x x 2 = 4 3 3(69x ) =4 x 2 4 x 2 27x+18 =0 4 x 2 24x3x+18 =0 4x(x6 ) 3(x6 ) =0 (x6 ) (4x3 ) =0 x6 =0 x 1 =6 4x3 =0 x 2 = 3 4
  13. x+2 x +x = 74 x x+2+ x 2 x = 74 x x+2+ x 2 74 =0 x 2 +x72 =0 (x+9 ) (x8 ) =0 x8 =0 x 1 =8 x+9 =0 x 2 =9
  14. (x+2 ) 2 2x5 3 =3 3 (x+2 ) 2 2x+5 3 =3 3( x 2 +4x+4 ) 2x+5 =9 3 x 2 +12x+122x+59 =0 3 x 2 +10x+8 =0 3 x 2 +6x+4x+8 =0 3x(x+2 ) +4(x+2 ) =0 (x+2 ) (3x+4 ) =0 x+2 =0 x 1 =2 3x+4 =0 x 2 = 4 3
  15. x x2 +x = 3x+15 4 x+x(x2 ) x2 = 3x+15 4 x+ x 2 2x x2 = 3x+15 4 x 2 x x2 = 3x+15 4 4( x 2 x ) =(x2 ) (3x+15 ) 4 x 2 4x =3 x 2 +15x6x30 4 x 2 4x3 x 2 9x+30 =0 x 2 13x+30 =0 (x10 ) (x3 ) =0 x10 =0 x 1 =10 x3 =0 x 2 =3
  16. 6 x4 4 x = 5 12 6x4(x4 ) x(x4 ) = 5 12 6x4x+16 x 2 4x = 5 12 12(2x+16 ) =5( x 2 4x ) 24x+192 =5 x 2 20x 0 =5 x 2 20x24x192 5 x 2 44x192 =0 5 x 2 60x+16x192 =0 5x(x12 ) +16(x12 ) =0 (x12 ) (5x+16 ) =0 x12 =0 x 1 =12 5x+16 =0 x 2 = 16 5
  17. (x2 ) 3 (x3 ) 3 =37 [(x2 ) (x3 ) ] [ (x2 ) 2 +(x2 ) (x3 ) + (x3 ) 2 ] =37 [ x 2 4x+4+ x 2 5x+6+ x 2 6x+9 ] =37 3 x 2 15x+1937 =0 3 x 2 15x18 =0 Dividiendo la ecuación para 3 x 2 5x6 =0 (x6 ) (x+1 ) =0 x6 =0 x 1 =6 x+1 =0 x 2 =1
  18. x1 x+1 2 = x+3 3 x12(x+1 ) x+1 = x+3 3 x12x2 x+1 = x+3 3 x3 x+1 = x+3 3 3(x3 ) =(x+3 ) (x+1 ) 3x9 = x 2 +4x+3 3x9 x 2 4x3 =0 x 2 7x12 =0 x 2 +7x+12 =0 (x+4 ) (x+3 ) =0 x+4 =0 x 1 =4 x+3 =0 x 2 =3
  19. 4x1 2x+3 = 2x+1 6x+5 (4x1 ) (6x+5 ) =(2x+1 ) (2x+3 ) 24 x 2 +20x6x5 =4 x 2 +8x+3 24 x 2 +14x54 x 2 8x3 =0 20 x 2 +6x8 =0 Dividiendo la ecuación para 2 10 x 2 +3x4 =0 10 x 2 5x+8x4 =0 5x(2x1 ) +4(2x1 ) =0 (2x1 ) (5x+4 ) =0 2x1 =0 x 1 = 1 2 5x+4 =0 x 2 = 4 5
  20. 3x+2 4 =5 9x+14 12x 3x+2 4 = 60x9x14 x 3x+2 = 51x14 3x 3x(3x+2 ) =51x14 9 x 2 +6x51x+14 =0 9 x 2 45x+14 =0 9 x 2 3x42x+14 =0 3x(3x1 ) 14(3x1 ) =0 (3x1 ) (3x14 ) =0 3x1 =0 x 1 = 1 3 3x14 =0 x 2 = 14 3