Question

The A.M. of two numbers exceed their G.M. by $3/2$ and the G.M. exceed their H.M. by $6/5$, find the sum of the two numbers ?

Answer 1

We have $A-G=1.5$ and $G-H=1.2$
Also we now $H=\frac{G^2}{A}$
Thus, we get $G-\frac{G^2}{A}=1.2$
$\Rightarrow \frac{G}{A}(A-G)=1.2$
$\Rightarrow 5G=4A$ and also $A-G=1.5$
$\therefore A=7.5,G=6$
Hence we get the numbers to be $12,3$