# Prove the following solutions..

• Sep 27th 2010, 07:02 PM
yess
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
• Sep 27th 2010, 07:19 PM
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Quote:

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).
• Sep 27th 2010, 07:42 PM
Prove It
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 $\displaystyle x = \frac{3}{2}$.
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