MathDB
2x^2 - 3xy + 2y^2 = 1, y^2 - 3yz + 4z^2 = 2, z^2 + 3zx - x^2 = 3$

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2019 Shortlist A2 day1

September 22, 2021
algebrasystem of equations

Problem Statement

Let x,y,z∈Rx, y, z \in R, find all triples (x,y,z)(x, y, z) that satisfy the following system of equations:
2x2−3xy+2y2=12x^2 - 3xy + 2y^2 = 1 y2−3yz+4z2=2y^2 - 3yz + 4z^2 = 2 z2+3zx−x2=3z^2 + 3zx - x^2 = 3
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