UZ-MO 2014 Problem 3

For all $x,y,z\in \mathbb{R}\backslash \{1\}$ , such that $xyz=1$ , prove that $\frac{x^2}{(x-1)^2}+\frac{y^2}{(y-1)^2}+\frac{z^2}{(z-1)^2}\ge 1$

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.