[SOLVED] Find the real roots...

**looi76** · March 29th 2008, 02:45 PM

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

**Plato** · March 29th 2008, 02:55 PM

Can you solve $18+x^2=4x^4$ ?
Hint: $4x^4 -x^2 -18 = (4x^2-9)(x^2+2)$ .

**mr fantastic** · March 29th 2008, 02:57 PM

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?)

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