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Given two real numbers p and q such that 1/p + 1/q = 1 and pq = 9, what is p + q?

 Jun 29, 2021
 #1
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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.

 Jun 29, 2021
 #2
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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

 Jun 29, 2021

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