Question

Find the real or imaginary solutions of the equation by factoring. X^4-10x^2=-9

Answer 1

Given expression is
`x^4-10x^2=-9`

Rearranging to get
`x^4-10x^2+9=0`

Let
`x^2` be
`p`, then we have
`p^2-10p+9=0`

Factorising we get
`(p-1)(p-9)=0`
Solving for
`p`, we have
`p=1` and
`p = 9`

Rewriting
`p` back as
`x^2`, we have:

`x^2=1` and
`x^2=9`

`x= √(1)` and
`x= √(9)`

`x = (+1) and (-1)` and
`x=(+3) and (-3)` ⇒ Final answers