olymmath

ILL 1985 Problem 79

    Let a,ba, b , and cc be real numbers such that 1bc−a2+1ca−b2+1ab−c2=0.\frac{1}{bc-a^2} + \frac{1}{ca-b^2}+\frac{1}{ab-c^2} = 0. Prove that a(bc−a2)2+b(ca−b2)2+c(ab−c2)2=0.\frac{a}{(bc-a^2)^2} + \frac{b}{(ca-b^2)^2}+\frac{c}{(ab-c^2)^2} = 0.

    Dataset text AI-MO AoPS. Quoted with source.

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