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#1 2011-07-18 00:32:14

Thanh Vān
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Nice Inequality

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

 

#2 2011-07-18 02:16:24

gAr
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Re: Nice Inequality

Hi Thanh Vān,

Welcome to the forum!

Last edited by gAr (2011-07-18 02:19:09)


"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."
 

#3 2011-07-18 10:28:37

Thanh Vān
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Re: Nice Inequality

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

 

#4 2011-07-18 13:07:26

gAr
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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."
 

#5 2011-07-18 21:00:15

bobbym
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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#6 2011-07-20 00:39:08

Thanh Vān
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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.

 

#7 2011-07-20 20:10:34

gAr
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Re: Nice Inequality

Hi Thanh Vān,

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



and



But unable to get anywhere.

Last edited by gAr (2011-07-22 15:02:17)


"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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