Middle European Mathematical Olympiad 2016 Problem T-1

AlgebraSystems

Determine all triples (a,b,c)(a, b, c) of real numbers satisfying the system of equations a2+ab+c=0,a^2 + ab + c = 0, b2+bc+a=0,b^2 + bc + a = 0, c2+ca+b=0.c^2 + ca + b = 0.