Question

How do you solve `\root[ 4] { 4- 5x ^ { 2} } = x`?

Answer 1

`x in {sqrt{(-5 + sqrt 41)/2}} subset RR`

Explanation:

`4 -5 x^2 = x^4`

`4 -5 y = y^2 and y = x^2`

`y^2 + 5y - 4 = 0`

`Delta = 25 + 4 * 1 * 4 = 41`

`y = (-5 ± sqrt 41)/2 = x^2 > 0`