Question

The difference of the reciprocals of two consecutive integers is 1/72. What are the two integers?

Answer 1

Answer :

Let two consecutive integers be x and (x+1)

Therefore from the question ,

1/x -1/(x+1) = 1/72

By taking LCM ,

x^2 + x -72 = 0

So solving this quadratic eq ,

We get

x = 8 , -9 (neglect)

Second integer = x +1 = 8+1 = 9