olymmath

JBMO-SL 2009 A4

Real numbers x,y,zx, y, z satisfy

0<x,y,z<10<x, y, z<1

and

xyz=(1−x)(1−y)(1−z).x y z=(1-x)(1-y)(1-z) .

Show that

14≤max⁡{(1−x)y,(1−y)z,(1−z)x}\frac{1}{4} \leq \max \{(1-x) y,(1-y) z,(1-z) x\}

Dataset text NuminaMath olympiads. Quoted with source.

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