INEQUALITY'S BLOG

July 11, 2011

Problem 226 (van khea)

Filed under: Problem by Van Khea — KKKVVV @ 11:29 pm

Let \displaystyle a, b, c>0\& a^{\frac{2}{3}}+b^{\frac{2}{3}}+c^{\frac{2}{3}}=3. Prove that: \displaystyle \frac{a^{\frac{2}{3}}}{\sqrt{b+c}}+\frac{b^{\frac{2}{3}}}{\sqrt{c+a}}+\frac{c^{\frac{2}{3}}}{\sqrt{a+b}}\geq \frac{3}{\sqrt{2}}

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