The T(h)rees

Algebra Level 3

Consider three real numbers (x,y,z)(x,y,z) such that

x39y=y39z=z39x=6\dfrac{x^3 - 9}{y} = \dfrac{y^3 - 9}{z} = \dfrac{z^3 - 9}{x} = 6

Evaluate xy+yz+zxx^y + y^z + z^x.

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