olymmath

JBMO-SL 2017 A4

Let x,y,zx, y, z be three distinct positive integers. Prove that

(x+y+z)(xy+yz+zx−2)≥9xyz(x+y+z)(x y+y z+z x-2) \geq 9 x y z

When does the equality hold?

Dataset text NuminaMath olympiads. Quoted with source.

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