Problem

Source: Indonesia TST 2016 Round 3

Tags: algebra, system of equations



Determine all triples of real numbers $(x, y, z)$ which satisfy the following system of equations: \[ \begin{cases} x+y+z=0 \\ x^3+y^3+z^3 = 90 \\ x^5+y^5+z^5=2850. \end{cases} \]