What is the resistance of each of the two resistors if a resistance of 50 ohms is obtained with

What is the resistance of each of the two resistors if a resistance of 50 ohms is obtained with a series connection, and 12 ohms with a parallel connection?

Data: Rpos. (serial connection) = 50 ohms; Rpar. (parallel connection) = 12 ohms.
1) Serial connection: Rpos. = R1 + R2, whence R1 = Rpos. – R2 = 50 – R2.
2) Parallel connection: Rpar. = R1 * R2 / (R1 + R2) = R1 * R2 / 50 = 12, whence R1 * R2 = 600.
3) Let’s make a quadratic equation: (50 – R2) * R2 = 600; 50R^2-R2^2 = 600; R2^2 – 50R^2 + 600 = 0.
By Vieta’s theorem: R1 = 20 ohms R2 = 30 ohms.
Check: Rpos. = 20 + 30 = 50 Ohm; Rpar. = 20 * 30 / (20 + 30) = 600/50 = 12 ohms.