INEQUALITY'S BLOG

August 7, 2011

Problem 247 van khea

Filed under: Problem by Van Khea — KKKVVV @ 1:26 am

Let a, b, c be positive real numbers such that a\leq b\leq c\&ab+bc+ca=1. Prove that

\displaystyle \frac{(ab)^{\frac{2}{3}}}{\sqrt{1+b^2}}+\frac{(bc)^{\frac{2}{3}}}{\sqrt{1+c^2}}+\frac{(ca)^{\frac{2}{3}}}{\sqrt{1+a^2}}\leq \sqrt[3]{\frac{9}{8}(a+b+c)}

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