Math Is Fun Forum
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#1 2014-01-13 00:26:51

Agnishom
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Conditional Identities

If a^2 + b^2 + c^2 = 1

Then, fill up the following:

__ < ab+bc+ca < __


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Who are you to judge everything?' -Alokananda

#2 2014-01-13 00:43:39

Nehushtan
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Re: Conditional Identities



This is attained when
.

By the Cauchy–Schwarz inequality,



This is attained when
.

Hence
.


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#3 2014-01-13 13:44:18

Agnishom
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Re: Conditional Identities

thanks


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Who are you to judge everything?' -Alokananda

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