IrMO 1992 Problem 2

How many ordered triples $(x,y,z)$ of real numbers satisfy the system of equations $x^2+y^2+z^2=9,$ $x^4+y^4+z^4=33,$ $xyz=-4?$

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.