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

Question

Question

Answer 1

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