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Means - Arithmetic, Geometric, and Harmonic

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

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A
$a$
💡 Explanation:

Here, $n=2$

$x _1=\dfrac{a}{1-ab}$ and $x _2=\dfrac{a}{1+ab}$
Then, $\dfrac{1}{x _1}=\dfrac{1-ab}{a}$ and $\dfrac{1}{x _2}=\dfrac{1+ab}{a}$

$\Rightarrow$  Harmonic mean $=\dfrac{n}{\dfrac{1}{x _1}+\dfrac{1}{x _2}}$

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

                                  $=\dfrac{2a}{2}$

                                  $=a$

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