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Let x,y and z be positive real numbers such that xyz=1. Prove that


\frac{x^{3}}{(1 + y)(1 + z)}+\frac{y^{3}}{(1 + z)(1 + x)}+\frac{z^{3}}{(1 + x)(1 + y)}  \geq \frac{3}{4}.

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