If the arithmetic mean of two numbers a and b, a > b > 0, is five times their geometric mean, then a+b/a-b is equal to.

Let a and b be the two positive numbers.
Arithmetic Mean = (a+b)/2
Geometric Mean = √ab
(a+b)/2 = 5√ab
a+b = 10√ab
(a+b)² = 100ab
(a-b)² = (a+b)² - 4ab = 100ab - 4ab = 96ab
Now,
(a+b)/(a-b) = √((a+b)²/(a-b)²) = √(100ab/96ab) = √(100/96) = √(25/24) = 5√(1/24) = 5√6/12 = 5√612