DE-MO 2005 Problem 1

Find all pairs (x; y) of real numbers satisfying the system of equations

$x^3 + 1 - xy^2 - y^2 = 0$ ; $y^3 - 1 - x^2y + x^2 = 0$ .

Darij

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.