2

Part of 2021 Canadian Mathematical Olympiad Qualification

Problems(1)

Symmetrical system of equations

Source: Canada Repêchage 2021/2 CMOQR

Determine all integer solutions to the system of equations: \begin{align*} xy + yz + zx &= -4 \\ x^2 + y^2 + z^2 &= 24 \\ x^{3} + y^3 + z^3 + 3xyz &= 16 \end{align*}

algebrasystem of equationsCanadarepechage