# Find x

• Jun 2nd 2010, 05:49 PM
windia
Find x
X^(4/3) - 6X^(2/3) = -8

and

9^(2x) - 2*9^x = 3

Thanks!! :D
• Jun 2nd 2010, 06:20 PM
TKHunny
These are simple quadratic forms. You must see the relationship to all other quadratics you have encountered.

$\displaystyle a\cdot Something^{2}\;+\;b\cdot Something\;+\;c\;=\;0$

Then, $\displaystyle Something\;=\;\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$

This should be familiar.
• Jun 2nd 2010, 06:44 PM
windia
Thanks!
• Jun 2nd 2010, 06:46 PM
TKHunny
Write it in that form. Show us your efforts and additional suggestions can be offered.

Hint: $\displaystyle 9^{2x}\;=\;\left(9^{x}\right)^{2}$
• Jun 2nd 2010, 06:53 PM
windia
For the first equation, I got down to x^4 - 6x^2 + 2 = 0 , am I doing it right so far? :D
• Jun 2nd 2010, 07:08 PM
TKHunny
That would depend on your substitution. What did you do? Normally, you would want to change variables. Using 'x' both before and after is certainly bad form, but mostly it's just confusing.

Try $\displaystyle y = x^{2/3}$ and write the whole thing in terms of 'y'.
• Jun 2nd 2010, 07:16 PM
windia
Ohhhh haha I got them now :D !! Should have thought of substitution :p