Mathematics - Sequence & Series Question with Solution | TestHub

Arithmetic Mean $=\frac{a+b}{2}$
Geometric Mean $=\sqrt{ab}$

$\Rightarrow \frac{a+b}{2}=5\sqrt{ab}$
$\Rightarrow a+b=10\sqrt{ab}$

$\Rightarrow (a+b{)}^2=100ab$

$\Rightarrow (a-b{)}^2=(a+b{)}^2-4ab=96ab$

Now,

$\Rightarrow \frac{a+b}{a-b}=\sqrt{\left(\frac{(a+b{)}^2}{(a-b{)}^2}\right)}=\sqrt{\frac{100}{96}}$

$=\frac{5\sqrt{6}}{12}$