<u>Given</u>:
Let the 3 consecutive even integers be x, x + 2 and x + 4.
Given that the sum of the squares of the first and the second integers is 2 more than the third integer.
We need to determine the 3 consecutive integers.
<u>Value of x:</u>
From the given, the expression can be written as,
Simplifying, we get;
Factoring the middle term, we get;
Since, the fraction is neither a even nor odd integer.
Thus, the value of x is -2.
<u>Consecutive integers:</u>
Substituting the value of x in the consecutive integers x, x + 2 and x + 4, we get;
Thus, the 3 consecutive integers are -2, 0 and 2.