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#1 2011-07-17 02:32:14

Thanh Vân
Member
Registered: 2011-07-17
Posts: 10

Nice Inequality

Let a,b,c,d be positive real numbes. prove that

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#2 2011-07-17 04:16:24

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Nice Inequality

Hi Thanh Vân,

Welcome to the forum!

Last edited by gAr (2011-07-17 04:19:09)


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#3 2011-07-17 12:28:37

Thanh Vân
Member
Registered: 2011-07-17
Posts: 10

Re: Nice Inequality

Oh. Hi gAr. I don't understand your proof.
Why you have

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#4 2011-07-17 15:07:26

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Nice Inequality

Hi,

I thought since 8 is the minimum value LHS can have, we may write like that.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#5 2011-07-17 23:00:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,719

Re: Nice Inequality

Hi;

For anyone else wishing to work on the problem here it is latexed.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#6 2011-07-19 02:39:08

Thanh Vân
Member
Registered: 2011-07-17
Posts: 10

Re: Nice Inequality

I thinks idea of gAr is wrong and can't use it to prove inequality. It can solve by Cauchy Schwarz Inequality and AM-GM Inequality very beautiful.

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#7 2011-07-19 22:10:34

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Nice Inequality

Hi Thanh Vân,

Yes, I was wrong. I made wrong assumption without checking.
Anyway, I could prove

and

But unable to get anywhere.

Last edited by gAr (2011-07-21 17:02:17)


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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