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#1 2011-07-18 10:33:52

Thanh Vān
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Inequality In [1;3]

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

Last edited by Thanh Vān (2011-07-18 10:34:34)

 

#2 2011-07-18 23:56:17

anonimnystefy
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Re: Inequality In [1;3]

hi Thanh Vān

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.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#3 2011-07-20 00:30:31

Thanh Vān
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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.

 

#4 2011-07-22 04:44:29

gAr
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Re: Inequality In [1;3]

Hi Thanh Vān,


"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 2011-07-22 21:14:20

Thanh Vān
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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.

 

#6 2011-07-22 21:25:12

gAr
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Re: Inequality In [1;3]

Hi Thanh Vān,

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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