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TH-TMO 2007 Problem 9

    Let f:R→Rf : R \to R be a function satisfying the equation f(x2+x+3)+2f(x2−3x+5)=6x2−10x+17f(x^2 + x + 3) + 2f(x^2 - 3x + 5) =6x^2 - 10x + 17 for all real numbers xx . What is the value of f(85)f(85) ?

    Dataset text AI-MO AoPS. Quoted with source.

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