The T(h)rees

Algebra Level 3

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

\[\dfrac{x^3 - 9}{y} = \dfrac{y^3 - 9}{z} = \dfrac{z^3 - 9}{x} = 6\]

Evaluate \(x^y + y^z + z^x\).

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