INEQUALITY'S BLOG

August 13, 2011

Problem 267 Van Khea

Filed under: Problem by Van Khea — KKKVVV @ 5:02 pm

Let $a, b, c$ be positive real numbers such that $a^2+b^2+c^2=3$. Prove that

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