+0

# algebra

0
193
2

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
+238
0

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
+510
+1

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