Expert: Scotto - 6/6/2009

Question
Hi,
I have a question I just cant finish. I am stuck somewhere.
The first part is fine. I am asked to express px-b=a-qx in terms of x. I work it out and get x=(a+b)/(q+p)
Then the next part states the following:
If SQRT(2p)=4a and q=-8b^2 show that 8x=1/(a-b)

So what I did first was express a in terms of p
[a=SQRT(2p)/4] and then b in terms of q
[b=SQRT(-q/8)

then I put these under 1 and worked out 8 times x from first part. I ended up with:
16/(2p+2q) = (8a+8b)/(q+p)
and then I got stuck and cant finish out the sum.
I had to square the left hand side earlier on to get rid of SQRT sign.
Would appreciate your help,
Annie

Answer
I'll read this much of your question:

I have a question I just cant finish. I am stuck somewhere.
The first part is fine. I am asked to express px-b=a-qx in terms of x. I work it out and get x=(a+b)/(q+p)
Then the next part states the following:
If SQRT(2p)=4a and q=-8b^2 show that 8x=1/(a-b)

and stop right there.

Not that we know that √(2p) = 4a and q = -8bČ.

We have q and we need to solve for p.

Squaring the equation √(2p) = 4a  on both sides gives
2p = 16aČ, so p = 8aČ.

Putting these both back in the equation gives us
x = (a+b)/(-8bČ + 8aČ).

Factoring out 8 in the denominator gives us x = (a+b)/(8(bČ-aČ)).

We know that bČ-aČ = (b+a)(b-a), so we have
x = (a+b)/(-8(b+a)(b-a).

It is also clear that the (a+b) is in both the numerator and the denominator, so we can see that x = 1/(-8(b-a)).

Moving the minus sign in the denominator gives us x = 1/(8(-b+a)),
which is the same as x = 1/(8(a-b)).

Multiplying both sides by 8 gives us 8x = 1/(a-b).

Hey, that's what were looking for!