Let and be positive real numbers such that . Prove that
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Let $x,y$ and $z$ be positive real numbers such that $xyz=1$. Prove that
$$\frac{x^{3}}{(1 + y)(1 + z)}+\frac{y^{3}}{(1 + z)(1 + x)}+\frac{z^{3}}{(1 + x)(1 + y)} \geq \frac{3}{4}.$$
Izvor: Međunarodna matematička olimpijada, shortlist 1998
Školjka 
and 
be positive real numbers such that 
. Prove that 