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#.