INEQUALITY'S BLOG

November 5, 2010

Problem 58 (Van Khea)

Filed under: the new math — KKKVVV @ 10:37 pm

Let a, b, c>0 ; ab+bc+ca=1. Prove that:

\displaystyle a^{\frac{5}{2}}\sqrt{b+c}+b^{\frac{5}{2}}\sqrt{c+a}+c^{\frac{5}{2}}\sqrt{a+b}\leq \frac{\sqrt{2}}{\sqrt[12]{3}}(a^3+b^3+c^3)^{\frac{2}{3}}

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