Given two real numbers p and q such that 1/p + 1/q = 1 and pq = 9, what is p + q?
+238 We can multiply the first equation by \(pq\),
\(1/p + 1/q = 1\)
\(q+p = pq\)
We know that \(pq\) is 9, therefore q + p, or p + q, is 9.
+514 it's a system of equations:
\(\frac{1}{p}+\frac{1}{q}=1\) and \(pq=9\)
\(p=\frac{9+3\sqrt{5}}{2}\)
\(q=\frac{9-3\sqrt{5}}{2}\)
the sum is 9
