CMO 1992 Problem 2

For $x,y,z \geq 0,$ establish the inequality

$x(x-z)^2 + y(y-z)^2 \geq (x-z)(y-z)(x+y-z)$

and determine when equality holds.

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.