The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers?

Question: The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers?Solution:Let the numbers be a and b. Then, a + b = 12 ab = 35∴ (a + b)/ab = 12/35⇒ a/ab + b/ab = 12/35∴ 1/b + 1/a = 12/35