. The effective capacitance of two capacitors, when connected in parallel is 32 μF and when connected in series is 6μF. What are the values of the two capacitors in μF?
a + b = 32 ... a = 32 - b
1/a + 1/b = 1/6 ... 6 a + 6 b = a b
substituting ... 192 - 6 b + 6 b = 32 b - b^2 ... b^2 - 32 b + 192 = 0
solve for b ... factoring or quadratic formula
... the two roots are the values for a and b