If H is the harmonic mean between p and q,the | vedclass

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(A) The harmonic mean $H$ between two numbers $p$ and $q$ is given by the formula:$H = \frac{2pq}{p + q}$We need to find the value of the expression $

Vedclass · Accepted Answer

$2$

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(A) The harmonic mean $H$ between two numbers $p$ and $q$ is given by the formula:$H = \frac{2pq}{p + q}$We need to find the value of the expression $\frac{H}{p} + \frac{H}{q}$.Substituting the value of $H$ into the expression:$\frac{H}{p} + \frac{H}{q} = \frac{1}{p} \left( \frac{2pq}{p + q} \right) + \frac{1}{q} \left( \frac{2pq}{p + q} \right)$Simplifying the terms:$= \frac{2q}{p + q} + \frac{2p}{p + q}$Combining the fractions since they have a common denominator:$= \frac{2q + 2p}{p + q}$$= \frac{2(p + q)}{p + q}$Canceling the common term $(p + q)$:$= 2$Thus,the correct option is $A$.

If $H$ is the harmonic mean between $p$ and $q$,then the value of $\frac{H}{p} + \frac{H}{q}$ is

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