# Thread: Prove the following solutions..

1. ## Prove the following solutions..

a) show that x^(-2/3) = 1/2 is x= square root (8)

b) 2x^3 - 3x^2 - 8x +12 = 0 are x = -2,2, 3/2

*dont just put the values of x into the equation..you need to prove itt

2. Originally Posted by yess
a) show that x^(-2/3) = 1/2 is x= square root (8)

b) 2x^3 - 3x^2 - 8x +12 = 0 are x = -2,2, 3/2

*dont just put the values of x into the equation..you need to prove itt
For the first one, consider what happens when you raise both sides to (-3/2).

3. b) $2x^3 - 3x^2 - 8x + 12 = 2x^3 - 8x - 3x^2 + 12$

$= 2x(x^2 - 4) - 3(x^2 - 4)$

$= (x^2 - 4)(2x - 3)$

$= (x-2)(x +2)(2x - 3)$.

Therefore if

$2x^3 - 3x^2 - 8x + 12 = 0$

$(x-2)(x+2)(2x-3) = 0$

$x - 2 = 0$ or $x+2 = 0$ or $2x - 3 = 0$

$x = 2$ or $x = -2$ or $x = \frac{3}{2}$.