FI-MO 2012 Problem 2

Let $x\ne 1,y\ne 1$ and $x\ne y.$ Show that if $\frac{yz-x^2}{1-x}=\frac{zx-y^2}{1-y},$ then $\frac{yz-x^2}{1-x}=\frac{zx-y^2}{1-y}=x+y+z.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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