for all values of x

find the value of p and q

I did

I'm stuck.. what should I do now, square route the whole thing?

edit:

whittled it down to

what now?

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- May 31st 2010, 09:20 AMMukilabFinding the values of p and q
for all values of x

find the value of p and q

I did

I'm stuck.. what should I do now, square route the whole thing?

edit:

whittled it down to

what now? - May 31st 2010, 09:27 AMUnknown008
The first expression you typed, is it supposed to be an equation?

If so, you can expand on the right hand side.

Giving

Then, equating the coefficients, you see that:

and

Or, you can take directly from where you reached;

and equate the coefficients.

:) - May 31st 2010, 09:33 AMMukilab
Thanks, so many people have told me about the coefficient and I've looked on sites but I still don't understand how to calculate it.

All I've learned is that comparing the coefficient is along the lines of ax^2+bx+c=a+b+c - May 31st 2010, 09:44 AMUnknown008
Okay, if you have

Then, a = p because both a and p are terms in x^2

b = q since both b and q are terms in x,

and c = r since both are independent terms. - May 31st 2010, 09:53 AMMukilab
That's what I was thinking about when I was doing the equation but I was unsure because it seems too perfect. Can you show me a proof?

- May 31st 2010, 10:18 AMUnknown008
I'm not good at proving things :o

Have you done vector coordinates yet?

If so, you should know, for example that if you have a vector (ai + bj) and another vector (xi + yj)

Given both are the same vectors, mean that ai + bj = xi + yj

Automatically, a will be equal to x and b will be equal to y.

I know, it's not a very convincing way, but I've learned it through practice :o - May 31st 2010, 10:21 AMMukilab
- June 1st 2010, 06:34 AMUnknown008
Ok, I thought more about it during the day. I'll use the method of completing the squares to prove it.

Let's have a look at:

I have to prove that a = p, b = q and c = r.

Now, completing the square;

So far so good.

For the equation to be true, either (a-p) = 0, or

I solve the first one.

a - p = 0

Therefore, a = p (1st shown)

Using that in the initial equation given,

Since a = p,

I put all the terms on the same side again.

Hence, b - q = 0, and b = q. (2nd shown)

Again, using this new result in the previous equation,

We get:

c = r

I hope this one satisfies you :) - June 1st 2010, 11:00 AMMukilab
Wow that really is something. Thanks for the effort you put in! It really settles my mind :P