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## #1 2013-09-19 00:04:25

Agnishom
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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'
'The whole person changes, why can't a habit?' -Alokananda

## #2 2013-09-19 00:13:01

bobbym

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### Re: Is it possible?

In mathematics, you don't understand things. You just get used to them.
No explanations, just DGA.
If you can not overcome with talent...overcome with effort.

## #3 2013-09-19 00:37:59

Agnishom
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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'
'The whole person changes, why can't a habit?' -Alokananda

## #4 2013-09-19 01:12:13

bobbym

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### Re: Is it possible?

I do not think so.

In mathematics, you don't understand things. You just get used to them.
No explanations, just DGA.
If you can not overcome with talent...overcome with effort.

## #5 2013-09-19 01:31:53

Agnishom
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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'
'The whole person changes, why can't a habit?' -Alokananda

## #6 2013-09-19 01:36:56

bobbym

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### Re: Is it possible?

You can find solutions if a = b.

In mathematics, you don't understand things. You just get used to them.
No explanations, just DGA.
If you can not overcome with talent...overcome with effort.

## #7 2013-09-19 01:46:54

Agnishom
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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'
'The whole person changes, why can't a habit?' -Alokananda

## #8 2013-09-19 02:00:19

bobbym

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### 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.
No explanations, just DGA.
If you can not overcome with talent...overcome with effort.

## #9 2013-09-19 02:56:57

anonimnystefy
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### 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.

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

## #10 2013-09-20 02:52:56

gAr
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### 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."

## #11 2013-09-20 05:47:37

anonimnystefy
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### Re: Is it possible?

Hi gAr

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

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

## #12 2013-09-23 13:01:37

Agnishom
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### 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 (2013-09-23 13:41:33)

'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'
'The whole person changes, why can't a habit?' -Alokananda