Question

Solve the following equation:
$\sqrt{x+5}+\sqrt{2x+7}=2\sqrt{x}$

Answer 1

Considering Domains

$x\ge 0$

Squaring on both sides

$⟹2\sqrt{(}2x^2+17x+35)=x-12$

squaring on both sides

$⟹8x^2+68x+140=x^2-24x+144$

$⟹7x^2+92x-4=0$

$⟹x=0.04,-13.18$

There is no such integer value for $x$