# INEQUALITY'S BLOG

## November 26, 2010

### Problem 72: van khea

Filed under: the new math — KKKVVV @ 8:52 am

Let $a, b, c$ be positive real numbers such that $a\geq b\geq c$ and $abc=1$. Prove that:
$\displaystyle \frac{a}{\sqrt{a+b}}+\frac{b}{\sqrt{b+c}}+\frac{c}{\sqrt{c+a}}\geq \frac{3}{\sqrt{2}}$