The sum of the reciprocals of two consecutive intergers is - 43 over 462 find the integers

Question

find the integers 

Answer 1

(1/n) + [1(n+1)] = -43/462

 

(2n + 1)/(n² + n) = -43/462

 

Cross multiply, expand and collect to get: 43n² + 967n + 462 = 0

 

The quadratic formula gives n = -22 and an extraneous root

 

The 2 integers are, therefore, -22 and -21

 

You should plug these numbers back into the original problem to be sure they work!