Given two real numbers 1 \(\frac{1}{p} + \frac{1}{q} = 1\) and \(pq = \frac{9}{2}\), what is q?
I can't figure out how to do this.. i keep ending up only knowing what \(q^2+p^2\) is, which is -9/2. was i supposed to go that way?
Try this:
Start with: pq = 9/2
Divide both sides by q : p = 9/(2q)
Substitute this into: 1/p + 1/q = 1
1/[9/(2q)] + 1/q = 1
2q/9 + 1/q = 1
Multiply by 9q: 2q2 + 9 = 9q
Rewrite: 2q2 - 9q + 9 = 0
Now finish with factoring or the quadratic formula.
ah thank you ok so q=3 and p=3/2 right?
Since it's symmetrical, there are two answers: q = 3 and p = 3/2 or p = 3 and q = 3/2
+261 
