Let $x, y, z \in R$, find all triples $(x, y, z)$ that satisfy the following system of equations: $2x^2 - 3xy + 2y^2 = 1$ $y^2 - 3yz + 4z^2 = 2$ $z^2 + 3zx - x^2 = 3$
Problem
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2019 Shortlist A2 day1
Tags: algebra, system of equations