Question

Resuelve cada ecuación completando un trinomio cuadrado perfecto. Porfavor
ayúdenme

Answer 1

Al resolver cada ecuación se obtiene:

a. x²+2x-15 = (x-3)(x+5)

b. x²-13x-30 = (x-10)(x-6)

c. 5x²-12x+4 = (x-5)(x-2/5)

d. 4x²+12x-16 = (x-1)(x+4)

e.. x²+10x-7 = (x+5-4√2)(x+5+4√2)

f. 9x²+10x+1 = (x+1/9)(x+1)

Explicación paso a paso:

La resolvente: x = (-b±√b²-4ac)/2a

a. x²+2x-15 =0

Aplicar la resolvente;

x = (-2±√2²-4(-15))/2

x = (-2±√64)/2

x = (-2±8)/2

x = 3

x =-5

x²+2x-15 = (x-3)(x+5)

   

b. x²-13x-30 =0

Aplicar la resolvente;

x = (13±√13²-4(-30))/2

x = (13±√49)/2

x = (13±7)/2

x = 10

x =6

x²-13x-30 = (x-10)(x-6)

c. 5x²-12x+4 =0

Aplicar la resolvente;

x = (12±√12²-4(5)(4))/10

x = (12±√64)/10

x = (12±8)/10

x = 2

x =2/5

5x²-12x+4 = (x-5)(x-2/5)

d. 4x²+12x-16 =0

Aplicar la resolvente;

x = (-12±√12²-4(-16)(4))/8

x = (-12±√400)/8

x = (-12±20)/8

x = 1

x =-4

4x²+12x-16 = (x-1)(x+4)

e. x²+10x-7 =0

Aplicar la resolvente;

x = (-10±√10²-4(-7))/2

x = (-10±√128)/2

x = (-10±8√2)/2

x = -5+4√2

x = -5-4√2

x²+10x-7 = (x+5-4√2)(x+5+4√2)

f. 9x²+10x+1 =0

Aplicar la resolvente;

x = (-10±√10²-4(9))/18

x = (-10±√64)/18

x = (-10±8)/18

x = -1/9

x =-1

9x²+10x+1 = (x+1/9)(x+1)