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#1 2013-09-18 02:04:25

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
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Is it possible?

Is it possible that


Where a, b and c are distinct real numbers.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#2 2013-09-18 02:13:01

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 95,948

Re: Is it possible?


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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#3 2013-09-18 02:37:59

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,565
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Re: Is it possible?

I would also say no, because if it was yes Suman Sir would not have asked it.

I guess we will get to see some thing like sin θ > 2 as a result which is a contradiction


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#4 2013-09-18 03:12:13

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 95,948

Re: Is it possible?

I do not think so.


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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#5 2013-09-18 03:31:53

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,565
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Re: Is it possible?

then??


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#6 2013-09-18 03:36:56

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 95,948

Re: Is it possible?

You can find solutions if a = b.


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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#7 2013-09-18 03:46:54

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,565
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Re: Is it possible?

They are distinct.

Please solve the problem for me


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#8 2013-09-18 04:00:19

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 95,948

Re: Is it possible?

That is what I mean, the numerator is only equal to the denominator when a=b=c.

When a,b,c>0 it is easy to prove that fraction is greater than 1 therefore there can be no sin(θ).

This is equal to,

There is only equality when a=b=c which violates the given conditions. That completes the proof for a,b,c>=0

Or use the AMGM.

Now add up the 3 inequalities and divide by 2 and the result follows. There is only equality when a=b=c.


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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#9 2013-09-18 04:56:57

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,922

Re: Is it possible?

Hi Agnishom

Start with the known inequality (a-b)^2+(b-c)^2+(c-a)^2>0 for distinct real numbers a, b and c.


“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
The knowledge of some things as a function of age is a delta function.

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#10 2013-09-19 04:52:56

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

Re: Is it possible?

Suppose


then


"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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#11 2013-09-19 07:47:37

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,922

Re: Is it possible?

Hi gAr

That doesn't work for ab+bc+ac<0, but that case is done similarly.


“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
The knowledge of some things as a function of age is a delta function.

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#12 2013-09-22 15:01:37

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,565
Website

Re: Is it possible?

gAr wrote:

Suppose


then

Please tell me how did you get that?

Later edit: Sorry, got it from bobbym's last post

Last edited by Agnishom (2013-09-22 15:41:33)


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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