Math Is Fun Forum

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

Website

Solve for x!

[(a+b-x)/c]+[(a+c-x)/b]+[(c+b-x)/a]+[4x/(a+b+c)]=1
Tell me How u did it?
Pls elaborate
Cant Understand

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'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'
I'm not crazy, my mother had me tested.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Solve for x!

hi

Again, let's just check I've got the question

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Solve for x!

hi bobbym

How are you today?  Looks like I've lost this poster.  I'm not going to attempt this one until I know the problem is as posted because it looks horrid, don't you think.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solve for x!

Hi Bob;

If you think it looks horrible wait till you work on it a little bit.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Solve for x!

Hi,

I'm planning to wait until I know it's the right question.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Solve for x!

Actually, cancel that.  I just took an intelligent guess and got the right answer.

But I'm keeping it to myself 'cos it makes me feel superior.  :)

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solve for x!

Hi Bob;

I have the answer too but I am afraid I am having a bit of a problem algebraically proving it.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Solve for x!

Hi bobbym

Oh! Now I don't feel superior any more.

If you've got a value, substitute it in and show that LHS = RHS.

Since it's a linear equation, one solution = the solution.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Solve for x!

Hi,

*deleted the answer*

Last edited by gAr (2011-01-30 02:21:58)

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solve for x!

I do not think so...

Hi Bob;

Yes, you could do that but people always ask that silly question, "how did you get that?" Then I am dead.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Solve for x!

hi bobbym and gAr

Since it's a linear equation, one solution = the solution.

How do you justify it?

Well, it is 'symmetrical' in a, b and c (by which I mean, if you swap all instances of, say, a with those of, say, b, the equation is unchanged.

So the 'answer' must also be symmetrical; ie.  whatever the 'a' bit looks like, the 'b' and 'c' bits will look the same.  So that answer is an intelligent guess.

gAr: I wasn't putting up the answer just yet because I was waiting for the OP to come back.  Otherwise, why are we spending time on his problem? (except obviously, it's lovely to chat to you all).  As he is off-line, you could edit it out now we've seen it.

Cannot find a smily for 'being conspiratorial'

Bob

Last edited by Bob (2011-01-30 02:01:59)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solve for x!

I get that urge a hundred times a day.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Solve for x!

Hi bob,

I am also having problem to solve it!
But I remember I had it in high school, it's a matter of taking common factor out. Cannot find the common factor!

---

"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."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Solve for x!

I'm adding it to my ever growing list of problems I'll come back to.

Bye for now,

Bob 

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solve for x!

See you Bob, have a good day!

Hi Agnishom;

The algebraic solution is very difficult.

This trick was shown to me by Subrata:

Add 3 to both sides. And distribute a one to each term on the LHS.

Thanks to him I can complete the problem!

Bring the 4 over from the RHS and combine it with the last term on the LHS.

It is substitution time! s = a + b + c:

Times both sides by abcs:

Factor:

So:

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Solve for x!

Here we go .....

separate the x and non x terms

move non x terms to RHS, and start to simplify

cancel abc from all denominators

put LHS over common denominator

simplify abc terms on LHS and cancel remainder of bracket with RHS, bring a+b+c across

Bob

Last edited by Bob (2011-01-30 05:00:01)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Solve for x!

Strictly (read the title of this thread)

Bob

ps  Am working on some new Smilies

pps gAr: Sorry I feel guilty now.  I asked you to remove the answer and I've gone and plastered it back on.  I'll work on a "Guilty look" Smily first.  Meanwhile best fit =

Put your answer back and then it shows you have prior claim.

Last edited by Bob (2011-01-30 05:18:31)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solve for x!

Hi gAr;

Why did you remove the answer? It was okay to leave it.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Solve for x!

hi bobbym

My fault I'm afraid.

Post #11

gAr: I wasn't putting up the answer just yet because I was waiting for the OP to come back.  Otherwise, why are we spending time on his problem? (except obviously, it's lovely to chat to you all).  As he is off-line, you could edit it out now we've seen it.

I was getting a bit irritated that while I was answering

http://www.mathisfunforum.com/viewtopic.php?id=14992

and suggesting the OP use Latex, yet another question was being constructed; again without a clear statement of what the question was.

(In fact, we still don't know for sure that this was the question.)

Then, while I was asking if I'd got the question correctly formulated, the OP logged out.

My apologies that I let that irritation show.

me =

Well anyway;  plenty of help given, so it would be nice to get a response, wouldn't it?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solve for x!

Oh, that is what you were talking about! I thought you were talking to me about editing the OP's post. To make it look like the way we want it to. That is why I said I have that urge a hundred times a day.

So they were right, first I must read the reply and then I must correctly understand it. Seems like a lot of work.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Solve for x!

Hi bobbym and bob,

It's okay, let's forget it.
Guessing the answer was easy

(In fact, we still don't know for sure that this was the question.)

I'm sure the question is correct. I've seen it before.

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solve for x!

I remember it too. But I do not know where. I think from the way he bracketed it that is what he meant.

Also I think the problem should state a,b,c are positive.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Solve for x!

This is wolframalpha's output : x = a+b+c and (a*b*c)*(a+b+c)≠0

---

"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."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Solve for x!

hi

True.  'a' etc not zero is required to manipulate the equation at all, so I took it as given.  Otherwise you get divide by zero problems in the original format.

Why do they have to be positive?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solve for x!

Hi Bob

Why do they have to be positive?

Because it can be manipulted to:

That is why Wolfram says (a*b*c)*(a+b+c)≠0

And that is why I said a,b,c have to be positve. Only with some of them being negative can (a*b*c)*(a+b+c) = 0.

So it appears as posed the problem is incomplete.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.