Question

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` ?

Answer 1

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`.