Question

The numbers whose A.M. is $34$ and G.M. is $16$ is ___.

Answer 1

Given,

$AM=\frac{a+b}{2}=34\Rightarrow a+b=68$

$GM=\sqrt{ab}=16\Rightarrow ab=256$

$a(68-a)=256$

$a^2-68a+256=0$

$(a-4)(a-64)=0$

$\therefore a=4,64$

when $a=4\to b=64$

when $a=64\to b=4$