Question

If the arithmetic mean of two numbers $a$ and $b$, $a > b > 0$, is five times their geometric mean, then $\frac{a + b}{a - b}$ is equal to :

• A. $\frac{\sqrt{6}}{2}$
• B. $\frac{3\sqrt{2}}{4}$
• C. $\frac{7\sqrt{3}}{12}$
• D. $\frac{5\sqrt{6}}{12}$

Answer 1

Answer: (D)

$\frac{a+b}{2} = 5\sqrt{ab}$
$\frac{a+b}{\sqrt{ab}} = 10$
$\therefore \quad \frac{a}{b} = \frac{10+\sqrt{96}}{10-\sqrt{96}} = \frac{10+4\sqrt{6}}{10-4\sqrt{6}}$
Use C and D
$\frac{a+b}{a-b} = \frac{20}{8\sqrt{6}} = \frac{5}{2\sqrt{6}} = \frac{5\sqrt{6}}{12}$