Question

if the a.m of two number is 4.5 and their h.m is 4 then find numbers

Answer 1

let numbers be a and b, then

Arithmetic Mean :

a+b / 2 = 4.5 or a+b = 9----I

Harmonic Mean :  2ab / (a+b) = 4

or ab=18 ----II

We have the sum and product from I and II, we need to find the a and b.

We will do it using Algebraic identity, (a+b)^{2}  - (a-b)^{2}  = 4ab

9^{2} - (a-b)^{2} = 4(18)       a-b=3 ----III

Solve I and III for value of a and b

we get a=6 and b=3