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

Let a,b,c be real numbers in [1;3]. prove that

*Last edited by Thanh Vân (2011-07-17 12:34:34)*

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

hi Thanh Vân

i tried to find the maximum value of the left part which is for a=b=c=3 and equals (3√2)/2, and the minimum value of the right part which is for a=b=c=1 and equals (9√2)/2 ,so for any other possible values for a,b and c the inequality will always be true.i think this is not the prefered method for solving this kind of problems but it is the only one i could come up with.

Here lies the reader who will never open this book. He is forever dead.

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

Hi anonimnystefy.

Look my inequality, you can see Maximun of left Inequality is when a=b=c=3 and minimum right inequality is same as yourself.

But it is very easy to talk so.

I thinks it is a problem very very nice, and we can solve it by basic 's inequality.

Maybe it is CS and AM-GM.

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

Hi Thanh Vân,

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

Hi gAr, I don't see you completed solution for my inequality (=left your proven). Please see again your post. Thanks.

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

Hi Thanh Vân,

Yes, I saw that after posting.

I'll try again sometime later.

"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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