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

  1. 2
  2. PQ/(P + Q)
  3. (P + Q)/PQ
  4. None of these

Answer (Detailed Solution Below)

Option 1 : 2
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Detailed Solution

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Concept:

If H is the Harmonic mean of numbers a and b and is given by

 \({\rm{H}} = \frac{{2{\rm{ab}}}}{{{\rm{a}} + {\rm{b}}}}\)

Calculation:

Given that,

H is the harmonic mean between P and Q.

\(⇒\ \frac{2}{H}=\frac{1}{p}+\frac{1}{Q}\)

⇒ H/P + H/Q = 2

Additional Information AM, GM, Formulas:

If A is the arithmetic mean of numbers a and b and is given by

⇔ \({\rm{A}} = \frac{{{\rm{a\;}} + {\rm{\;b}}}}{2}\)

If G is the geometric mean of the numbers a and b and is given by 

⇔ \({\rm{G}} = \sqrt {{\rm{ab}}} \)

Relation between AM, GM and HM

1. G2 = AH

2. AM  ≥  GM  ≥  HM

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