CGMO 2009 Problem 5

Let $x,y,z$ be real numbers greater than or equal to $1.$ Prove that $\prod(x^{2} - 2x + 2)\le (xyz)^{2} - 2xyz + 2.$

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.