Problem

Source:

Tags: inequalities



Let $a$, $b$ and $c$ be non-negative numbers such that $ab+ac+bc+abc=4.$ . Prove that:

HIDE: $$\sqrt{\frac{ab+ac+1}{a+2}}+\sqrt{\frac{ab+bc+1}{b+2}}+\sqrt{\frac{ac+bc+1}{c+2}}\leq3.$$PS Dedicated to dear KhuongTrang