MEMO 2016 T1

Find all triples $(a, b, c)$ of real numbers such that $a^2 + ab + c = 0,$ $b^2 + bc + a = 0,$ $c^2 + ca + b = 0.$

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.