for all values of x
find the value of p and q
I'm stuck.. what should I do now, square route the whole thing?
whittled it down to
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,
c = r
I hope this one satisfies you