INEQUALITY'S BLOG

November 21, 2010

Problem 61: van khea

Filed under: Uncategorized — KKKVVV @ 6:20 am

5) Let a, b, c>0 ; a^3+b^3+c^3=3 ; x, y, z\in (0, 1) ; x^3+y^3+z^3=2 ។ Prove that:
\displaystyle \frac{a^3}{\sqrt{(1+ab^2)(1+xy^2)}}+\frac{b^3}{\sqrt{(1+bc^2)(1+yz^2)}}+\frac{c^3}{\sqrt{(1+ca^2)(1+zx^2)}}\geq \frac{9\sqrt{2}}{10}\sqrt{1+xyz}

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