Given a, b, c as real numbers such that a2 + b2 + c2 = 1
Prove that 2(1 + a)(1 + b)(1 + c) ≥ abc
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Codeforces (c) Copyright 2010-2024 Михаил Мирзаянов
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Auto comment: topic has been updated by cheater2k (previous revision, new revision, compare).
may be missing some conditions ? I got abc > = 2√3 - 1 which is wrong ofcourse
Cauchy inequality？
I can't understand the relation between codeforces and proving an equality????
Someone has answered the question over here
I'll write the answer here again -
You can consider the sign of abc. If abc≥0, then the required result follows. If abc < 0, it suffices to show that (1 + a)(1 + b)(1 + c)≥0.