The sum of the reciprocals of 2 consecutive integers is 9/20. Find the numbers.

Question

The sum of the reciprocals of 2 consecutive integers is 9/20. Find the numbers.

Answer 1

If the two nun=mbers are x and x+1, the reciprocals of these are 1/x and 1/(x+1)

 

Therefore the equation is 1/x + 1/(x + 1) = 9/20.

 

Multiply this equation by the Least Common denominator 20(x)(x+1).

 

This becomes 20(x)(x+1)/x + 20(x)(x+1)/(x+1) = 9(20)(x)(x+1)/20

 

Simplifying:  20(x+1) + 20(x) = 9(x)(x+1)

 

And we get 20x + 20 + 20x = 9x² + 9x.

 

Set equal to 0:  9x²-31x - 20 = 0

 

Factor:  (9x -  5)(x - 4) = 0.  Solve for the integer x.

 

I hope this helps.