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1998 IMO Shortlist Problems/A3

Revision as of 00:30, 19 December 2021 by Bluesoul (talk | contribs)

Let $x,y,z$ be positive real numbers such that $xyz=1$. Prove that $\frac{x^3}{(1+y)(1+z)}+\frac{y^3}{(1+x)(1+z)}+\frac{z^3}{(1+x)(1+y)}\geq\frac{3}{4}$

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