INEQUALITY'S BLOG

November 5, 2010

Inequality: Problem 53

Filed under: the new math — KKKVVV @ 1:43 pm

(VanKhea):

Let a, b, c>0 ; a^2+b^2+c^2+ab+bc+ca=1. Prove that:

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

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