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?
I'm not good at proving things
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
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