cheater2k's blog

A beautiful Inequality
By cheater2k, history, 9 years ago, In English

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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9 years ago, # |
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Auto comment: topic has been updated by cheater2k (previous revision, new revision, compare).

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9 years ago, # |
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may be missing some conditions ? I got abc  >    =  2√3  -  1 which is wrong ofcourse

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9 years ago, # |
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Cauchy inequality？

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9 years ago, # |
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I can't understand the relation between codeforces and proving an equality????

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9 years ago, # |
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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.

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