Question

If two numbers have arithmetic mean 2700 and harmonic mean 75, find their geometric mean

Answer 1

Hello,

Assume a and b the 2 numbers.


`(a+b)/(2)=2700\\ (1)/(a) + (1)/(b)= (2)/(75)\\ a+b=2*2700\\\\ (a+b)/(ab) = (2)/(75) ==\ \textgreater \ 75*(a+b)=2ab\\\\ 2ab=75*2*2700\\\\ ab=75*2700=202500\\\\ \boxed{ √(ab) =450}\\`