Question

Solve for x.
\[x^4( {18 \over x^4} + {1 \over x^2})=4(x^4)\]

Answer 1

\[4x^4 - x^2 -18 =0\]

Answer 2

this has real and complex roots

Answer 3

@order put \(x^2=u\)
then \(x^4=u^2\)
Now our equation becomes a quadratic equation
\[4u^2-u-18=0\]
Can you solve now?

Answer 4

Yes I think so. Let me try.

Answer 5

Got it, thanks :)

Answer 6

(18/x^2)+(1) = 4x^2

18 + x^2 = 4 x^4

4x^4 - x^2 - 18 = 0

(x^2 + 2)(4x^2 - 9)

x^2 = -2
OR
x^2 = 9/4 ==> x = +- 3/2