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a^2 + b^2 + c^2 = 1 , a(2b - 2a - c) >= 1/2

Source: 2022 NZMO - New Zealand Maths Olympiad Round 2 p2

October 8, 2022
algebrainequalities

Problem Statement

Find all triples (a,b,c)(a, b, c) of real numbers such that a2+b2+c2=1a^2 + b^2 + c^2 = 1 and a(2b−2a−c)≥12a(2b - 2a - c) \ge \frac12.
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