7
$\begingroup$

Let $a,b,c, >0$ be real numbers such that $$\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}\ge3$$

How to prove that :

$$\frac{(ab+b)(2b+1)}{(ab+a)(5b+1)}+\frac{(bc+c)(2c+1)}{(bc+b)(5c+1)}+\frac{(ca+a)(2a+1)}{(ca+c)(5a+1)}\ge\frac{3}{2}$$

  • 0
    It comes from here http://www.fen.bilkent.edu.tr/~cvmath/Problem/problem_2011.htm (April 2011)2012-09-02

2 Answers 2