KöMaL 2017 C1401

The positive numbers $x$ , $y$ satisfy the equation $x^3+y^3=x-y$ . Prove that $x^2+y^2<1$ .

Official text KöMaL. 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.