two unknown resistors a and b are connected together. when they are connected in series their combined resistance is 15 ohm. When they are connected in parallel, their combined resistance is 3.3 ohm. What are the resistances of A and B?

Answer 1

R1+R2 = 15 Ohms

R1*R2/(R1+R2) = 3.3 Ohms

In Eq2, replace R1+R2 with 15 Ohms:
R1*R2/(15) = 3.3
R1*R2 = 49.5
R1 = 49.5/R2

In Eq1, Replace R1 with 49.5/R2:
(49.5/R2)+R2 = 15
R2^2 + 49.5 = 15R2
R2^2 - 15R2 + 49.5 = 0
Use Quad. Formula:
R2 = 10.1 Ohms

R1 + 10.1 = 15
R1 = 4.9 Ohms