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 | Let <math>x,y.z</math> be positive real numbers such that <math>xyz=1</math>. Prove that | ||
| − | <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> | + | <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> |
Revision as of 00:30, 19 December 2021
Let 
be positive real numbers such that 
. Prove that
$\frac{x^3}{(1+y)(1+z)}+\frac{y^3}{(1+x)(1+z)}+\fra{z^3}{(1+x)(1+y)}\geq\frac{3}{4}$ (Error compiling LaTeX. Unknown error_msg)
