Between what two consecutive integers is 15 and 16

10 and 11

13 and 14

12 and 13

C. 13 and 14

Step-by-step explanation:

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.

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).

Many people prefer to solve this problem in a short way.

   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.

Solved and explained in detailed and short modes.

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square

the answers c