Question

Solve :
$x^4-5x^2+6=0$

Answer 1

Let $x^2=a$

so, $x^4-5x^2+6=0\Rightarrow (x^2{)}^2-5(x^2)+6=0\Rightarrow a^2-5a+6=0$

$\Rightarrow a^2-3a-2a+6=0\Rightarrow a(a-3)-2(a-3)=0\Rightarrow (a-3)(a-2)=0$

Either $a=3$ or $a=2$ thus, $x=\sqrt{3}$ or $x=\sqrt{2}$