Quadratic System of Equations

Algebra Level 4

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

Details and Assumptions:

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

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