JEE Main On 8 April 2017 Question 15
Question: If the arithmetic mean of two numbers and b,a, > b > 0. Is five times their geometric mean, then $ \frac{a+b}{a-b} $ is equal to: [JEE Online 08-04-2017]
Options:
A) $ \frac{7\sqrt{3}}{12} $
B) $ \frac{3\sqrt{2}}{4} $
C) $ \frac{\sqrt{6}}{2} $
D) $ \frac{5\sqrt{6}}{12} $
Show Answer
Answer:
Correct Answer: D
Solution:
- $ \frac{a+b}{2}=5\sqrt{ab} $ $ \frac{a+b}{\sqrt{ab}}=10 $
$ \therefore $ $ \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} $
