3

Part of 2003 Canada National Olympiad

Problems(1)

2 equations, 3 variables

Source: Canada 2003

Find all real positive solutions (if any) to \begin{align*} x^3+y^3+z^3 &= x+y+z, \mbox{ and} \\ x^2+y^2+z^2 &= xyz. \end{align*}

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