# INEQUALITY'S BLOG

## October 3, 2011

### Problem 307 Van Khea

Filed under: Problem by Van Khea — KKKVVV @ 7:13 pm

if $a, b, c$ are positive real numbers such that $abc=1$. Prove that:

$\displaystyle \frac{1}{a\sqrt{1+3b}}+\frac{1}{b\sqrt{1+3c}}+\frac{1}{c\sqrt{1+3a}}\geq \frac{3}{2}$