# INEQUALITY'S BLOG

## December 8, 2011

### Problem 309 van khea

Filed under: Problem by Van Khea — KKKVVV @ 6:48 am

If $a, b, c$ are positive real numbers such that $a+b+c=3$. Prove that
$\sqrt{1+a^4}+\sqrt{1+b^4}+\sqrt{1+c^4}\leq \sqrt{2}(a^2+b^2+c^2)$