# [SOLVED] Find the real roots...

• March 29th 2008, 02:45 PM
looi76
[SOLVED] Find the real roots...
Question:
Find the real roots of the equation $\frac{18}{x^4} + \frac{1}{x^2} = 4$
• March 29th 2008, 02:55 PM
Plato
Can you solve $18+x^2=4x^4$?
Hint: $4x^4 -x^2 -18 = (4x^2-9)(x^2+2)$.
• March 29th 2008, 02:57 PM
mr fantastic
Quote:

Originally Posted by looi76
Question:
Find the real roots of the equation $\frac{18}{x^4} + \frac{1}{x^2} = 4$

Multiply through by x^4 and re-arrange to get $4x^4 - x^2 - 18 = 0$.

Let $w = x^2$ and solve $4w^2 - w - 18 = 0$ for w.

Then solve $x^2 = w$ for x (you'll only use one of the solutions of w to get real roots - why?)