olymmath

USAMO 2013 Problem 4

  • Day 2

Find all real numbers x,y,z≥1x,y,z\geq 1 satisfying min⁡(x+xyz,y+xyz,z+xyz)=x−1+y−1+z−1.\min(\sqrt{x+xyz},\sqrt{y+xyz},\sqrt{z+xyz})=\sqrt{x-1}+\sqrt{y-1}+\sqrt{z-1}.

Dataset text AI-MO AoPS. Quoted with source.

Also USAJMO 2013 Problem 6.

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