INEQUALITY'S BLOG

November 5, 2010

Inequality: Problem 50

Filed under: the new math — KKKVVV @ 12:40 pm

(Van Khea): Let a, b, c\geq 0. Prove that:

\displaystyle a^{\frac{4}{3}}\sqrt{b+c}+b^{\frac{4}{3}}\sqrt{c+a}+c^{\frac{4}{3}}\sqrt{a+b}\leq \frac{\sqrt{2}}{\sqrt{3}}(a+b+c)^{\frac{7}{6}}\sqrt[3]{a^2+b^2+c^2}

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