TR-MO 2011 Problem 3

$x,y,z$ positive real numbers such that $xyz=1$ Prove that: $\frac{1}{x+y^{20}+z^{11}}+\frac{1}{y+z^{20}+x^{11}}+\frac{1}{z+x^{20}+y^{11}}\leq1$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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