Answer: The consecutive integers are 7 and 8.
Step-by-step explanation: a= the first integer, (a+1)= the second integer
Therefore,
a^2 + (a+1)^2= 113
= a^2 + a^2+2a+1 = 113
= 2a^2+ 2a -112 = 0
Using the quadratic equation you get 7 and 8
As a checkpoint:
7^2 + 8^2 = 113
= 49 + 64 = 113
= 113 = 113