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possible values of xy+yz+zx when x^2-yz = y^2-zx = z^2-xy = 2

Source: Czech-Polish-Slovak Match Junior 2019, team p4 CPSJ

January 20, 2020
algebrasystem of equations

Problem Statement

Determine all possible values of the expression xy+yz+zxxy+yz+zx with real numbers x,y,zx, y, z satisfying the conditions x2−yz=y2−zx=z2−xy=2x^2-yz = y^2-zx = z^2-xy = 2.
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