INEQUALITY'S BLOG

July 29, 2010

(van khea):Problem 023

Filed under: Uncategorized — KKKVVV @ 1:19 am

Let x, y, z>0; xyz=1. Prove that:

\displaystyle \frac{\biggl(\frac{1}{x^{2}}+\frac{1}{y}\biggl)^{2011}}{x(y+z)}+\frac{\biggl(\frac{1}{y^{2}}+\frac{1}{z}\biggl)^{2011}}{y(z+x)}+\frac{\biggl(\frac{1}{z^{2}}+\frac{1}{x}\biggl)^{2011}}{z(x+y)}\geq 3.2^{2010}

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