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:

Step-by-step solution

Arithmetic Mean = a + b 2 Geometric Mean = a b ⇒ a + b 2 = 5 a b ⇒ a + b = 10 a b ⇒ ( a + b ) 2 = 100 a b ⇒ ( a - b ) 2 = ( a + b ) 2 - 4 a b = 96 a b Now, ⇒ a + b a - b = ( a + b ) 2 ( a - b ) 2 = 100 96 = 5 6 12