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## #1 2014-01-13 00:26:51

Agnishom
Real Member

Online

### 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
Power Member

Offline

### Re: Conditional Identities

This is attained when
.

By the Cauchy–Schwarz inequality,

This is attained when
.

Hence
.

## #3 2014-01-13 13:44:18

Agnishom
Real Member

Online

### 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