What are two consecutive integers whose product is 72?



    What is asked in the problem? and Given:

       two consecutive numbers whose sum is 72





Representation:

   Let n = the first number

      n + 1 = the second consecutive number



The product of the numbers is 72

   n (n+1) = 72     

   n^2 + n = 72

  n^2 + n - 72 = 0          factor 

  (n + 9)(n-8) = 0

n + 9 = 0     n - 8 = 0

 n = -9         n = 8



n+1 = -8        n = 9



There are two solutions:

1. the first integer is -9 and the next one is -8.

2. the first integer is 8 and the next one is 9.

    

 



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