Question

If the arithmetic mean of two positive numbers a & b (a > b) is twice their G.M., then a:b is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$\frac{a+b}{2}=2\sqrt{ab}$
$a+b-4\sqrt{ab}=0$
$\frac{a}{b}+1-4\sqrt{\frac{a}{b}}=0$ (Dividing by b)
Or ${\left(\sqrt{\frac{a}{b}}\right)}^2-4\sqrt{\frac{a}{b}}+1=0$
$\therefore \sqrt{\frac{a}{b}}=\frac{4\pm 2\sqrt{3}}{2}=(2\pm \sqrt{3})$
$\frac{a}{b}=\frac{2+\sqrt{3}}{2-\sqrt{3}}$