Question

Solve ${\left(\frac{1}{2}\right)}^{x^6-2x^4}<2^{x^2}$

Answer 1

${\left(\frac{1}{2}\right)}^{x^6-2x^4}<2^{x^2}$
$2^{2x^4-x^6}<2^{x^2}$
$\Rightarrow 2x^4-x^6<x^2$
$\Rightarrow 2x^4-x^6-x^2<0$
$\Rightarrow x^6-2x^4+x^2>0$
$\Rightarrow x^2(x^4-2x^2+1)>0$
$\Rightarrow x^2(x^2-1{)}^2>0$

$x=(-\infty ,+\infty )$