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x^2 + y^2 + z^2 if x^2=2 + y , y^2=2 + z , z^2=2 + x

Source: V- Rioplatense 1996 L3 P3

September 19, 2022
algebrasystem of equations

Problem Statement

The real numbers x,y,zx, y, z, distinct in pairs satisfy {x2=2+yy2=2+zz2=2+x.\begin{cases} x^2=2 + y \\ y^2=2 + z \\ z^2=2 + x.\end{cases} Find the possible values of x2+y2+z2x^2 + y^2 + z^2.
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