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#1 2009-07-09 21:04:58

tony123
Member
Registered: 2007-08-03
Posts: 229

pozitive real numbers

Let

be pozitive real numbers satisfying



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#2 2009-07-10 04:49:26

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: pozitive real numbers

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#3 2009-07-10 09:43:54

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: pozitive real numbers

Hi Jane;

Thanks for the link.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#4 2009-07-10 21:04:38

tony123
Member
Registered: 2007-08-03
Posts: 229

Re: pozitive real numbers

TheAbstractionist;337552 wrote:

By AM–GM, we have


and




Also, note that

is positive (because, by AM–GM,
So, multiplying the above two inequalities gives


Hence

Similarly,

and


(by inequality of arithmetic and harmonic means)[/indent]

Multiplying through by

will give the required inequality.

Last edited by tony123 (2009-07-10 21:13:05)

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