Question

The harmonic mean of $\frac{a}{1-ab}$ and $\frac{a}{1+ab}$ is

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

Answer 1

Answer: (A)

$a$

Here, $n=2$

$x_1=\frac{a}{1-ab}$ and $x_2=\frac{a}{1+ab}$

Then, $\frac{1}{x_1}=\frac{1-ab}{a}$ and $\frac{1}{x_2}=\frac{1+ab}{a}$

$\Rightarrow$ Harmonic mean $=\frac{n}{\frac{1}{x_1}+\frac{1}{x_2}}$

$=\frac{2}{\frac{1-ab}{a}+\frac{1+ab}{a}}$

$=\frac{2a}{2}$

$=a$