Suppose A.M. of two positive numbers be 7 and G.M. between them be 5. The A.M. between their squares  is 

Let two positive numbers be a, b. Then  

$a+b=2\left(7\right)=14$ and $\sqrt{ab}=5$ or $ab=25$

Now, $a^2+b^2=(a+b{)}^2-2ab=196-50=146$

$\Rightarrow \frac{1}{2}\left(a^2+b^2\right)=73$