Question

The harmonic mean of $\frac{a}{1-ab}$ and $\frac{a}{1+ab}$ is
[MP PET 1996; Pb. CET 2001]

• A. $\frac{a}{\sqrt{1-a^2{b}^2}}$
• B. $\frac{a}{1-a^2{b}^2}$
• C. a
• D. $\frac{1}{1-a^2{b}^2}$

Answer 1

The correct option is C a

$H.M.=\frac{2\left(\frac{a^2}{1-a^2{b}^2}\right)}{\frac{a}{1-ab}+\frac{a}{1+ab}}=\frac{2a^2}{2a}=a.$