When faced with the problem: “The sum of two numbers is 10, and their product is 20. Can you find the sum of the reciprocals of these numbers?”—many might think of solving it using simultaneous equations. However, there is a quicker and more elegant method.

Step 1: Let’s define the two numbers as ‘a ‘and ‘ b ‘.

Given:  a + b = 10 (sum of the numbers)

ab = 20 (product of the numbers)

Step 2: We are asked to find the sum of the reciprocals of these numbers, which is given by:

Step 3: Notice that: after taking LCM

Step 4: Substitute the known values:

a + b = 10 (sum of the numbers)

ab = 20 (product of the numbers)

Final Answer: The sum of the reciprocals of the two numbers is

1/2

This clever method avoids the more tedious algebraic manipulations and gets you directly to the answer in just a few steps!