INEQUALITY'S BLOG

August 19, 2011

Problem 299 Van Khea

Filed under: Problem by Van Khea — KKKVVV @ 5:51 am

Let a, b, c be positive real numbers such that a^4+b^4+c^4=3. Prove that

\displaystyle \frac{a^3}{\sqrt{b^4+c^4}}+\frac{b^3}{\sqrt{c^4+a^4}}+\frac{c^3}{\sqrt{a^4+b^4}}\geq \frac{3}{\sqrt{2}}

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