Ejercicio 272

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CAPITULO XXXIII

Ecuaciones incompletas de segundo grado
Ejercicio 272
Resolver las ecuaciones:
  1. x 2 =5x x 2 5x =0 x(x5 ) =0 x 1 =0 x5 =0 x 2 =5
  2. 4 x 2 =32x 4 x 2 +32x =0 4x(x+8 ) =0 4x =0 x 1 =0 x+8 =0 x 2 =8
  3. x 2 3x =3 x 2 4x x 2 3 x 2 +4x3x =0 2 x 2 +x =0 x(2x+1 ) =0 x 1 =0 2x+1 =0 2x =1 x 2 = 1 2
  4. 5 x 2 +4 =2(x+2 ) 5 x 2 + 4 =2x+ 4 5 x 2 2x =0 x(5x2 ) =0 x 1 =0 5x2 =0 5x =2 x 2 = 2 5
  5. (x3 ) 2 (2x+5 ) 2 =16 x 2 6x+9(4 x 2 +20x+25 ) =16 x 2 6x+94 x 2 20x25 =16 3 x 2 26x 16 = 16 3 x 2 +26x =0 x(3x+26 ) =0 x 1 =0 3x+26 =0 3x =26 x 2 = 26 3
  6. x 2 3 x9 6 = 3 2 Multiplicando la ecuación por 6 2 x 2 x+ 9 = 9 x(2x1 ) =0 x 1 =0 2x1 =0 2x =1 x 2 = 1 2
  7. (4x1 ) (2x+3 ) =(x+3 ) (x1 ) 8 x 2 +12x2x 3 = x 2 +2x 3 8 x 2 +10x x 2 2x =0 7 x 2 +8x =0 x(7x+8 ) =0 x 1 =0 7x+8 =0 7x =8 x 2 = 8 7
  8. x+1 x1 x+4 x2 =1 (x+1 ) (x2 ) (x+4 ) (x1 ) (x1 ) (x2 ) =1 x 2 x2( x 2 +3x4 ) =(x1 ) (x2 ) x 2 x2 x 2 3x +4 = x 2 3x +2 0 = x 2 +x+ 2 2 0 =x(x+1 ) x 1 =0 0 =x+1 x 2 =1