Mathematics

Problem

The combined resistance

R

of two resistors

R_1

and

R_2

where

R_1, R_2 > 0

is given by

\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}

. If

R_1 + R_2 = C

(constant), show that the maximum resistance

R

is obtained by choosing

R_1 = R_2