Question

(4x-9)³=-125 necesito saber la respuesta

Answer 1

(2x + 3) ^ 3 = -125

2x + 3) ^ 3 + 125 = 0

(2x + 3) ^ 3 + 5 ^ 3 = 0 ===> La suma de dos cubos.

A ^ 3 + B ^ 3 = (A + B) (A ^ 2 - AB + B ^ 2)

[(2x + 3) +5] [(2x + 3) ^ 2 - (2x + 3) .5 + 5 ^ 2] = 0

[2x + 8] [4x ^ 2 + 12x + 9 - 10x - 15 + 25] = 0

[2x + 8] [4x ^ 2 + 2x + 19] = 0

(I) 2x + 8 = 0, o (Ii) 4x ^ 2 + 2x + 19 = 0

(I) 2x + 8 = 0 ==> 2x = -8 ==> x = -4

(II) 4x ^ 2 + 2x + 19 = 0

x = [-2 +/- sqrt [2 ^ 2 - 4 (4) (19)] / 2 (4)

x = [-2 +/- sqrt (4 - 304)] / 8

x = [-2 +/- sqrt (-300)] / 8 = [-2 +/- sqrt (300) (- 1)] / 8

x = [-2 +/- (10sqrt 3) i] / 8

Entonces: x = -4; x = [- 2 + (10sqrt 3)] / 8; x = [- 2 - (10sqrt 3)] / 8