Question

The difference of two natural numbers is 3 and the difference of their reciprocals is . Find the numbers.

Answer 1

The numbers are 4 and 7.

Step-by-step explanation:

Let the natural numbers be x and y.

Given:

x - y = 3

y = x -3 -------------(1)

1/x - 1/y = 3/28 -------------(2)

Substituting y = x-3 in (2), we get:  

1/x + 1/x-3 = 3/28

28 (x - 3 - x) = 3(x²-3x)

-84  = -9x + 3x²

3x² -9x + 84 = 0

Dividing by 3, we get:  x² -3x +28 = 0

x² -7x + 4x +28 = 0

x (x - 7) +4 (x - 7) = 0

(x + 4) (x -7) = 0

x can be -4 or +7.

So Y can be -7 or +4

Hence the numbers are 4 and 7.