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jcherry99
Givens
r1 + r2 = 18
r1*r2 / (r1 + r2) = 4

Sub and Solve
There are many ways to proceed. I like to find r1*r2 and that simplifies things.

substitute 18 for r1 + r2
r1*r2 / 18 = 4 multiply by 18
r1 * r2 = 4 * 18
r1 * r2 = 72

Now you can set up a quadratic. Using r1 + r2 = 18, solve for r1
r1 = 18 - r2

Substitute into r1*r2 = 72
r2*(18 - r2) = 72                Remove the brackets.
18r2 - (r2)^2 = 72              Bring the left side over to the right side.
0 = (r2)^2 - 18r^2 + 72

This factors
(r2 - 12)(r2 - 6) = 0
r2 - 12 = 0
r2 = 12
or
r2 - 6 = 0
r2 = 6

r1*r2 = 72
r1*12 = 72
r1 = 72 / 12
r1 = 6

r1 = 12 when r2 = 6. 

Answers
r1 = 12
r2 = 6

or

r1 = 6
r2 = 12 

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