# INEQUALITY'S BLOG

## August 19, 2011

### Problem 298 Van Khea

Filed under: Problem by Van Khea — KKKVVV @ 3:12 am

Let $a, b, c, d$ be positive real numbers such that $a+b+c+d\leq 4$.Prove that

$\displaystyle \frac{1}{a^4+b^4+c^4+d^4}+\frac{1}{abcd}\geq \frac{5}{4}$