INEQUALITY'S BLOG

August 1, 2010

Problem 030

Filed under: Uncategorized — KKKVVV @ 12:25 am

Let a, b,c be positive real numbers satisfying a\geq b\geq c and abc=1. Prove that:

\displaystyle \frac{1}{a^2\sqrt{b+c}}+\frac{1}{b^2\sqrt{c+a}}+\frac{1}{c^2\sqrt{a+b}}\geq \frac{a}{\sqrt{b+c}}+\frac{b}{\sqrt{c+a}}+\frac{c}{\sqrt{a+b}}

 

Van Khea      

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