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#1 2014-01-12 01:26:51

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,560
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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.'
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#2 2014-01-12 01:43:39

Nehushtan
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Registered: 2013-03-09
Posts: 618
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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 2014-01-12 14:44:18

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,560
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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'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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