if

prove

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- Dec 29th 2007, 05:14 AMbobakInequality
if

prove - Dec 29th 2007, 05:29 AMPlato

Can you use this to complete the problem? - Dec 29th 2007, 06:24 AMbobak
- Dec 29th 2007, 06:50 AMJaneBennet
Use the Cauchy–Schwarz inequality:

Equality obtains if and only if the vectors and in are linearly dependent; i.e. if and only if . Since , this won’t happen and so the inequality is always strict. - Dec 29th 2007, 07:00 AMIsomorphism
- Dec 29th 2007, 07:13 AMJaneBennet
- Dec 29th 2007, 07:33 AMbobak
thanks Isomorphism, i am familiar with the AM-GM inequality but i was hoping this could be pulled out by fiddling.

JaneBennet the Cauchy–Schwarz inequality is totally alien to me, you know any good article with an explanation / proof of it ? - Dec 29th 2007, 07:34 AMIsomorphism
- Dec 29th 2007, 05:34 PMThePerfectHacker
- Dec 29th 2007, 06:10 PMIsomorphism
No, I used AM-GM to get the result.Perhaps I should be more clear.

By AM-GM,

Add them up,

Cancel 2 on both sides to wrap it up (Whew)

Yes I am aware that you can get it by a simple application of CS. But when we were in school we were taught only AM-GM. So I thought probably the poster wanted the proof using that :) - Dec 29th 2007, 06:14 PMThePerfectHacker
Or you can just use C-S: