Question

Solve : $x^4-6x^2+4$

Answer 1

$x^4-6x^2=4$

Let $x^2=a$

$\Rightarrow a^2-6a+4$

$\Rightarrow a=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\Rightarrow a=\frac{6\pm \sqrt{36-4\left(4\right)}}{2}$

$\Rightarrow a=\frac{6\pm \sqrt{20}}{2}=\frac{6\pm 2\sqrt{5}}{2}$

$\Rightarrow a=3\pm \sqrt{5}$

So $x^2=3\pm \sqrt{5}$

$\Rightarrow x=\pm \sqrt{3\pm \sqrt{5}}$.