PL-OM 1991 Problem 6

If $x, y, z$ are real numbers satisfying $x^2 +y^2 +z^2 = 2$ , prove the inequality $x + y + z \leq 2 + xyz$ When does equality occur?

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.