KöMaL 2006 B3945

Solve the following simultaneous equations: $x^3$ + $y^3$ + $z^3$ =8, $x^2$ + $y^2$ + $z^2$ =22, $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}+\frac{z}{xy} =0$ .

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