Question

Solve the following inequality:

$x^2\cdot 5^x-5^{(}2+x)<0$

Answer 1

$x^2{.5}^x<5^{2+x}⟹x^2<5^2$

we can get equality at $x=5$ when we compare terms on both sides

and LHS goes on decreasing on decreasing the value of x and satisfies the inequality

$⟹x\in (-\infty ,5)$