INEQUALITY'S BLOG

July 26, 2010

(Van Khea):Problem 006

Filed under: the new math — KKKVVV @ 4:01 pm

Let x, y, z\in {(0, 1)} ; x+y+z=1. Prove that:

\displaystyle \frac{x^{3}}{\sqrt{1-y^{2}}}+\frac{y^{3}}{\sqrt{1-z^{2}}}+\frac{z^{3}}{\sqrt{1-x^{2}}}\geq \frac{1}{6\sqrt{2}}

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