Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,840
Website

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'
'Humanity is still kept intact. It remains within.' -Alokananda

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,400

Re: Is it possible?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,840
Website

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'
'Humanity is still kept intact. It remains within.' -Alokananda

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,400

Re: Is it possible?

I do not think so.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,840
Website

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'
'Humanity is still kept intact. It remains within.' -Alokananda

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,400

Re: Is it possible?

You can find solutions if a = b.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,840
Website

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'
'Humanity is still kept intact. It remains within.' -Alokananda

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,400

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,307

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

Offline

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

gAr
Member
Registered: 2011-01-09
Posts: 3,478

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."

Offline

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,307

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

Offline

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,840
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'
'Humanity is still kept intact. It remains within.' -Alokananda

Offline

Board footer

Powered by FluxBB