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#1 2011-07-17 12:33:52

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

Inequality In [1;3]

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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#2 2011-07-18 01:56:17

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Inequality In [1;3]

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.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#3 2011-07-19 02:30:31

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

Re: Inequality In [1;3]

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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#4 2011-07-21 06:44:29

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

Re: Inequality In [1;3]

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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#5 2011-07-21 23:14:20

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

Re: Inequality In [1;3]

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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#6 2011-07-21 23:25:12

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

Re: Inequality In [1;3]

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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