# INEQUALITY'S BLOG

## August 3, 2011

### Problem 265 van khea

Filed under: Problem by Van Khea — KKKVVV @ 2:53 pm

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

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

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