The Arithmetic Mean (AM) of m , n and The Geometric Mean (GM) of a , b are equals to (ma+nb )/ (m+n) Then Answer the value of m and n by using a and b ?

1 Answer
Aug 11, 2018

The values of m and n are not determined by the values of a and b.

Explanation:

We are given:

(m+n)/2 = sqrt(ab) = (ma+nb)/(m+n)

We want to find m and n in terms of a and b, but note that if a=b and a > 0 then:

(ma+nb)/(m+n) = (ma+na)/(m+n) = a = sqrt(a^2)

and:

m+n = 2sqrt(a^2) = 2a

There is no more information we have about m and n except that m+n = 2a

So it is not possible to determine the value of m or n in terms of a and b.