Two resistors when connected in parallel give an equivalent resistance of 2 ohm and when connected in series they give an equivalen resistance of 9 ohm find the resistance of both the resistors?

(R1 * R2) / (R1 + R2) = 2 Parallel

R1 + R2 = 9 Series

Treating the two as simultaneous equations, and substituting for R1:

((9-R2) * R2) / (9 - R2 + R2) = 2

R2^2 - 9R2 + 18 = 0

Solving the quadratic, we get:

R2 = 6 ohm R1 = 3 ohm

Which you can check by substituting back into the original equations.