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Difference between revisions of "1998 IMO Shortlist Problems/A3"
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Let <math>x,y.z</math> be positive real numbers such that <math>xyz=1</math>. Prove that
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Let <math>x,y,z</math> be positive real numbers such that <math>xyz=1</math>. Prove that
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<math>\frac{x^3}{(1+y)(1+z)}+\frac{y^3}{(1+x)(1+z)}+\fra{z^3}{(1+x)(1+y)}\geq\frac{3}{4}</math>
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<math>\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}</math>

Revision as of 00:30, 19 December 2021

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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