olymmath

AUSTRIAN-POLISH 1985 Problem 1

    Show that if a+b+c=0a+b+c=0 then (ab−c+bc−a+ca−b)(b−ca+c−ab+a−bc)=9(\frac{a}{b-c}+\frac{b}{c-a}+\frac{c}{a-b})(\frac{b-c}{a}+\frac{c-a}{b}+\frac{a-b}{c})=9 .

    Dataset text AI-MO AoPS. Quoted with source.

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