Question

Solve the following inequalities.
$4^x-{5.2}^x-1>0.$

Answer 1

$4^x-{5.2}^x-1>0$

Let $k=2^x$

$2^{2x}-{5.2}^x-1>0$

$⟹k^2-5k-1>0$

$⟹k=\frac{5\pm \sqrt{29}}{2}$

Since,$k=2^x>0\forall x\in R$

$⟹k=\frac{5+\sqrt{29}}{2}$