OBM 2008 Problem 3

Let $x,y,z$ real numbers such that $x + y + z = xy + yz + zx$ . Find the minimum value of ${x \over x^2 + 1} + {y\over y^2 + 1} + {z\over z^2 + 1}$

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.