Solve `(x^2+2)^2+8x^2=6x(x^2+2)`

Answer

`x= 2 pm sqrt(2),x = 1 pmi`

Explanation

Given equation is `(x^(2) + 2)^(2) + 8x^(2) = 6x (x^(2) + 2)`
Dividing throughout by `x^(2)`, we get
`((x^(2)+2)/(x))^(2) + 8 = 6 ((x^(2)+2)/(x))`
`rArr t^(2) - 6t + 8 = 0 where t = (x^(2)+2)/(x)`
`therefore t = 4, t = 2`
`therefore (x^(2)+2)/(x) = 4 or x = 2 pmsqrt(2)`
and `(x^(2)+2)/(x) = 2 or x = pmi`