... equation ...

RauLiTo · 2006-05-31 21:03:59

hi guys ... how are you all ?

well ... my friend said that there is a solution for the equation :
3 / X = 4 / X ... i told him immediately thats impossible
whats ur opinion ? and if not why ?!:cool:

naturewild · 2006-05-31 21:09:43

x = 0 counts as a solution right?

RauLiTo · 2006-05-31 21:22:13

i don't think so !!!
we cant divide be zero !!! its unknown

naturewild · 2006-05-31 21:29:51

3/x = 4/x

is the same as

x/3 = x/4

So x = 0 works in this case

Or you can multiple the quesiton by x² and you will get 3x = 4x, which gives you x = 0.

numen · 2006-05-31 22:21:20

But if x=0 is a solution, the original question is invalid!

luca-deltodesco · 2006-05-31 23:20:33

numen wrote:

But if x=0 is a solution, the original question is invalid!

only if you dont like infinity

but really, i think you can say x = 0 is a solution.

as x approaches 0, the value of 4/x and 3/x both approach infinity, and become infintisamely different

Last edited by luca-deltodesco (2006-05-31 23:29:43)

Jai Ganesh · 2006-05-31 23:47:35

A simple solution:-

3X=4X

4X-3X=0

X=0

Simple, isn't it?

RauLiTo · 2006-05-31 23:55:58

no solution = anything expect the zero

MathsIsFun · 2006-06-01 00:43:54

Reductio Ad Absurdum (Proof by Contradiction):

Let us assume it is a true equation

Start with: 3/x = 4/x
Multiply both sides by x: 3=4

Awww, it din't work

So equation is invalid (within the rules of algebra anyway, but that doesn't rule it out completely)

George,Y · 2006-06-01 01:34:36

NO SOLUTION Because X in the equation do not have a defination on 0.

But you can just put a very large number (positive or negative) as a "solution".

When X is very large, the difference between 3/X and 4/X is very small, hence neglactable in some sense.

Praticly, think of a pair double stars from far far away, does the gravity from the two make any difference for you?

Still, I will not say the answer is infinity, since it is my belief to deny a single nonvariable infinity.

Ricky · 2006-06-01 06:32:17

When you simplify equations, you can gain solutions that weren't originally there.

For example:

y = x/x

If you try to graph that without simplifying first, you would get a line at y = 1 with a hole at zero. Because of this, upon simplification, we must say:

y = 1, except when x = 0.

The same must be done here as well.

John E. Franklin · 2006-06-01 08:08:21

luca-deltodesco wrote:

as x approaches 0, the value of 4/x and 3/x both approach infinity, and become infintisamely different

Anyone care to dispute this limit luca-deltodesco suggests is zero? I do.

Ricky · 2006-06-01 08:49:45

Sure.

luca-deltodesco · 2006-06-01 09:32:25

Ricky wrote:

Sure.

yeh i realised that about 20 minutes after i posted it, but the thread seemed to have came to an end, so i didnt change it

Ricky · 2006-06-01 12:24:04

Even worse is when you realize you made a really dumb mistake in a post you just wrote, but you know you won't have computer access for 5 hours and there is no way for you to change it. Those can be one of the longest times on earth.

krassi_holmz · 2006-06-02 05:24:43

For the limes thingy:
If

,
that doesn't imply:

and...again...NO SOLUTION!!!
(If there was some limmy solution, then all math theory would have been contradictory-and this would have been TERRIBLE!!)

John E. Franklin · 2006-06-02 15:25:08

Are you saying "limits" thingy, which means approaching an x number and coming as close as you can get to x which then suggests an f(x), but it might not be exactly the f(x) at the number x?

Nigel · 2006-06-02 16:10:09

x=0 or x=∞
I think...

Ricky · 2006-06-02 16:33:05

The only time that

is when f(x) is continuous at c. If it's not, then f(c) can be any value, including no value at all.

krassi_holmz · 2006-06-02 20:20:18

Consider a function: {x} - the real part of x. ({2.5}=0.5, {5/3}=1/3, {sqrt(2)}=sqrt(2)-1}).
Let see what's the limit as x goes to 2.
Here we have 2 different limits: left-limit and right-limit:

See? You can't conclude what is f(x) using only limits.
(and there are more interesting examples: the function

)

::Edited. Changed some latex text.

Last edited by krassi_holmz (2006-06-02 20:50:12)

Ricky · 2006-06-02 20:33:23

Just to let you know, you can use \mbox to put in text:

\mbox{if x is irrational}

Produces:

krassi_holmz · 2006-06-02 20:48:37

Thank you. I tryed with \text{...}, but it gave an error.

George,Y · 2006-06-03 01:43:15

krassi_holmz wrote:

For the limes thingy:
If
,
that doesn't imply:
and...again...NO SOLUTION!!!
(If there was some limmy solution, then all math theory would have been contradictory-and this would have been TERRIBLE!!)

No perfect solution.

But accepted solution. If you find a 0 on a calculator display credible for 0. Then there are many answers.

krassi_holmz · 2006-06-03 03:59:42

OK. x is not "exactly" null. But what's happening if x is infinitesimal?

George,Y · 2006-06-03 21:18:52

I don't know real infinity thing, what i know is an amount divided by a small number.

I find a case. do you think there is too much difference between enjoying Bill Gates' fortune and owning Warrant Buffet's investment?

Besides, it's not me who proposed infinity is an answer.

Anyway, to Raulito, if you accept some error and do not persuit absolute accuracy, there are accepted solutions.
Otherwise, there is none.

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