Question

The arithmetic mean of two number is 13/2 and their geometric mean is 6 find their harmonic mean

Answer 1

let the two nos. be a,b and c

A.M. = (a+c) / 2;  13/2 = (a+c) / 2
13 = a+c ---------(1)

G.Mean = $\sqrt{ac}$ ; 6 = $\sqrt{ac}$
 by squaring,

36 = ac -------------(2)

H.Mean = 2 / ($\frac{1}{c}$ + $\frac{1}{a}$)

on solving, we'll get 5.5384.
therefore H.Mean is 5.5384.