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Regional Olympiad - FBH 2018 Grade 9 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2018

September 18, 2018
algebraidentityreal numbers

Problem Statement

if aa, bb and cc are real numbers such that (a−b)(b−c)(c−a)≠0(a-b)(b-c)(c-a) \neq 0, prove the equality: b2c2(a−b)(a−c)+c2a2(b−c)(b−a)+a2b2(c−a)(c−b)=ab+bc+ca\frac{b^2c^2}{(a-b)(a-c)}+\frac{c^2a^2}{(b-c)(b-a)}+\frac{a^2b^2}{(c-a)(c-b)}=ab+bc+ca
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