SOLUTION: The product of 2 consecutive integers is 182. Find two pairs of integers that have this product. Give details.

    Let n be the smaller of the two consecutive integers.

    Then the other integer is  (n+1).


    We are given that  

       n*(n+1) = 182.


    Simplify

       n^2 + n - 182 = 0,

    Factor left side

       (n-13)*(n+14) = 0.


    The solutions are  n= 13  and  n= -14.


    You may check that both of them satisfy the problem' condition, giving you two answers

        the pair  (13,14)  and the pair  (-14,-13).

    They notice that the square root of 182 is between 13 an 14,

    and it gives them the idea that the numbers 13 and 14 are the solution.


    Then these people get the next idea that if the product of 13 and 14 is equal to 182,

    then the product of the opposite numbers is also 182, so


            both the pairs (13,14)  and  (-14,-13)  are solutions.