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  4. If H is the harmonic mean between P and Q, then the value of (H/P)+(H/Q) is

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Q. If $H$ is the harmonic mean between $P$ and $Q$, then the value of $ \frac{H}{P}+\frac{H}{Q}$ is

VITEEEVITEEE 2007

Solution:

Given : H is the harmonic mean between P & Q
$\therefore H=\frac{2PQ}{P+Q}\Rightarrow \frac{1}{H}=\frac{P+Q}{2PQ}$
$\Rightarrow \frac{2}{H}=\frac{1}{Q}+\frac{1}{P}\Rightarrow \frac{H}{P}+\frac{H}{Q}=2$