Two wires when connected in series have an equivalent resistance of 18ohm nd when in parallel an equivalent resistance of 4ohm find their resistance

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