ISL 1998 A3

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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