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
b) $\displaystyle 2x^3 - 3x^2 - 8x + 12 = 2x^3 - 8x - 3x^2 + 12$
$\displaystyle = 2x(x^2 - 4) - 3(x^2 - 4)$
$\displaystyle = (x^2 - 4)(2x - 3)$
$\displaystyle = (x-2)(x +2)(2x - 3)$.
Therefore if
$\displaystyle 2x^3 - 3x^2 - 8x + 12 = 0$
$\displaystyle (x-2)(x+2)(2x-3) = 0$
$\displaystyle x - 2 = 0$ or $\displaystyle x+2 = 0$ or $\displaystyle 2x - 3 = 0$
$\displaystyle x = 2$ or $\displaystyle x = -2$ or $\displaystyle x = \frac{3}{2}$.