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 $a and b$ ?

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Answer 1 · 2018-08-11T22:35:38

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

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 $b$ .

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