Question

Solve:$x^4-6x^2-16=0$

Answer 1

$x^4-6x^2-16=0$

$x^4-8x^2+2x^2-16=0$

$\Rightarrow x^2(x^2-8)+2(x^2-8)=0$

$\Rightarrow (x^2-8)(x^2+2)=0$

$\Rightarrow (x^2-{\left(2\sqrt{2}\right)}^2)(x^2+2)=0$

$\Rightarrow (x-2\sqrt{2})(x+2\sqrt{2})(x^2+2)=0$

$\therefore x=2\sqrt{2},-2\sqrt{2},\pm \sqrt{-2}$

$\therefore x=2\sqrt{2},-2\sqrt{2},i\sqrt{2},-i\sqrt{2}$

'