Quadratic System of Equations

Algebra Level 4

How many unordered triplets (x,y,z)(x,y,z) are in the range [0,2][0,2] and satisfy the system of equations: {2x2−4x+2=y2y2−4y+2=z2z2−4z+2=x\left\{\begin{array}{l}2x^2-4x+2=y\\ 2y^2-4y+2=z\\ 2z^2-4z+2=x\end{array}\right.

Details and Assumptions:

An unordered triplet means that (1,2,3)(1,2,3) is the same as (3,2,1)(3,2,1) or (1,3,2)(1,3,2).

Daniel Liu by Daniel Liu
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