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Regional Olympiad - FBH 2014 Grade 9 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2014

September 24, 2018
valuealgebra

Problem Statement

Find all possible values of (a+b−c)2(a−c)(b−c)+(b+c−a)2(b−a)(c−a)+(c+a−b)2(c−b)(a−b)\frac{(a+b-c)^2}{(a-c)(b-c)}+\frac{(b+c-a)^2}{(b-a)(c-a)}+\frac{(c+a-b)^2}{(c-b)(a-b)}
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