INEQUALITY'S BLOG

November 5, 2010

Inequality: Problem 54

Filed under: the new math — KKKVVV @ 1:53 pm

(Van Khea): Let a, b, c>0 ; a+b+c=a^2+b^2+c^2.

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{\sqrt{3}}{\sqrt{2}}\sqrt{a+b+c}

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