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triangle ABC, \alpha = 3\beta =>(a^2 -b^2)(a-b) = bc^2

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1997 p1

February 20, 2020
geometryangles

Problem Statement

Let ABCABC be a triangle with sides a,b,ca,b,c and corresponding angles α,βγ\alpha,\beta\gamma . Prove that if α=3β\alpha = 3\beta then (a2−b2)(a−b)=bc2(a^2 -b^2)(a-b) = bc^2 . Is the converse true?
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