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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: 90,489

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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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."

Offline

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