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

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Answer 1 · 2018-08-11T22:35:38

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

We are given:

$\frac{m + n}{2} = \sqrt{a b} = \frac{m a + n b}{m + n}$ $(m+n)/2 = sqrt(ab) = (ma+nb)/(m+n)$

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

$\frac{m a + n b}{m + n} = \frac{m a + n a}{m + n} = a = \sqrt{a^{2}}$ $(ma+nb)/(m+n) = (ma+na)/(m+n) = a = sqrt(a^2)$

and:

$m + n = 2 \sqrt{a^{2}} = 2 a$ $m+n = 2sqrt(a^2) = 2a$

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

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

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