Wikipedia:Reference desk/Archives/Mathematics/2010 February 8

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February 8

c / d = c + d ; slove for c. Too simple, right????

In my old Algebra text I came across this problem and now I am racking my brain trying to solve it. The book's answer section shows one solution but I keep getting multiple different solutions. Are there multiple outcomes for this, or am I just doing it incorrectly? Thank you. 161.165.196.84 (talk) 07:27, 8 February 2010 (UTC)

Can this be solved Quadratically? What am I missing here? 161.165.196.84 (talk) 07:56, 8 February 2010 (UTC)

Before I proceed with my post, I should note that it will be 100% effective to you only if you read it carefully in its entirety; note each paragraph and especially the comments in brackets. You are not obliged to read furthur than the steps outlined directly below but by reading my entire post, you will be able to solve problems of this nature in the future easily (and without any assistance). I have split the explanation directly below the outlined steps into paragraphs for greater readability. (Also, please do not remove your signature (i.e. your IP address) subsequent to your post; the presence of your signature is mandatory per WP:SIGN).

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${\frac {c}{d}}=c+d$

$c=cd+d^{2}$

$c-cd=d^{2}$

$c(1-d)=d^{2}$

$c={\frac {d^{2}}{1-d}}$

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As you may have noticed, "the secret" to these sorts of problems is to somehow separate one variable from the others, and in most cases, "removing fractions" is a first step towards this goal. In this case, therefore, the natural first step is to multiply both the left hand side, and the right hand side, by d; this removes the troublesome fraction. (Imagine that the fraction was not present; that is, we needed to solve for c in $c=c+d$. Obviously, this is easy, and we discover $c=0$. Thinking in this manner is very helpful because it tells you that the fraction is the only "bother", and thus the best way to solve the problem is to multiply by d on both sides of the equation (i.e. remove the fraction).)

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Once the fraction is removed, we return to the main purpose of this problem: the separation of one variable (c) from the others. And since the expression after the removal of the fraction is $c=cd+d^{2}$, a first step towards separating c from d is to place all "c terms" (that is, expressions like c and $cd$ (anything with a c in it)) to one side of the equation.

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Once this is done, we arrive at $c-cd=d^{2}$; at this stage the key point to note is the expression "$c-cd$". Experience tells you to write this as $c(1-d)$ (this "breaks" the expression into a c and something else ($1-d$) which can be placed elsewhere; namely to the other side of the equation).

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Once the $1-d$ is placed to the other side of the equation (by dividing both the left hand side and the right hand side by $1-d$), we make the transition from $c(1-d)=d^{2}$ to $c={\frac {d^{2}}{1-d}}$; observe that we have determined c (${\frac {d^{2}}{1-d}}$). PST 08:19, 8 February 2010 (UTC)

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This example illustrates the five steps (normally taken in order) to solve most linear and quadratic equations:

• clear fractions
• multiply out brackets
• collect terms
• factorise (spell this with a "z" if you live in the USA)
• divide

Dbfirs 18:58, 8 February 2010 (UTC)

What if d = 0? — Carl (CBM · talk) 19:02, 8 February 2010 (UTC)

It is implicitly assumed that $d\neq 0$; otherwise the equation is nonsensical in the reals. I agree, though, that this should be stated in the end. -- Meni Rosenfeld (talk) 19:30, 8 February 2010 (UTC)

...as well as $d\neq 1$ – otherwise dividing both sides by $d-1$ wouldn't make sense. By the way, we can show why d must be not equal to 1 if we plug it into the original equation: $d=1$ would make it read $c=c+1$ which would in turn imply $0=1.$
CiaPan (talk) 21:17, 8 February 2010 (UTC)

Mohamed Altoumaimi

Do you have any idea about this [1]? I found too many web articles when searching after "Mohamed Altoumaimi", but non of them seems to be a reliable source rather than a copy/paste rummer. There is even no further explanation what the 16 years old boy exactly did to simplify understanding Bernoulli number.--Email4mobile (talk) 21:13, 8 February 2010 (UTC)

I'd suggest to cut the Google URL to http://www.google.com/search?q=Mohamed+Altoumaimi – there's no need to make other browsers to pretend they are Mozilla Firefox...
CiaPan (talk) 21:20, 8 February 2010 (UTC)

Thankyou, for this info, CiaPan. I've modified it.--Email4mobile (talk) 21:27, 8 February 2010 (UTC)

If you'd looked at Bernoulli number just an hour or so ago there would have been a big blurb about him that someone just stuck in but but I've gone and deleted that. Surprising you've come here so shortly thereafter but that's coincidence for you. There was a discussion in the talk page of the article and it was deemed one of those news hype things which disappears after a week. Sixteen year old rediscovers some maths done a long time ago. It would be worth something in an interview about studying maths but that's about it. Dmcq (talk) 22:39, 8 February 2010 (UTC)

Well, I don't think it is just a coincidence but I was translating that article few months ago to Arabic and stopped but yesterday, I found some changes talking about that boy in the Arabic Wikipedia and I had to delete yesterday and add some explanation about the confusion (See the date it was changed by someone called Babylon56). —Preceding unsigned comment added by Email4mobile (talk • contribs) 11:08, 9 February 2010 (UTC)

One-to-one and differentiable function

Say a function is g(x). Then if there are two values of g(x) for one x, then is g(x) not 1-1? Please give an example of such fucntion. What if there is one g(x) for two or more x. eg. g(x)=x^2

Also, for a function g(x) to be differentiable, does it need to be differentiable at every x (domain)? —Preceding unsigned comment added by 142.58.43.83 (talk) 22:09, 8 February 2010 (UTC)

Two values of g(x) for one x is, by definition, not a function, much less a 1-1 function. If g(x)=g(y) for x≠y, then g is not 1-1, by definition. And for g to be differentiable, by definition, we require that it be differentiable at every point x in the domain. --COVIZAPIBETEFOKY (talk) 22:16, 8 February 2010 (UTC)