As the exercise suggests, let's call the two consecutive integers and [/tex] x+2 [/tex]. In fact, if
is even, the next number,
is odd, and the next number
is again even.
Moreover, since the two numbers are positive, the square of the bigger one is actually bigger, so the difference is
In fact, note that if the numbers were negative, for example -6 and -4, their squares would be 36 and 16, so you should have subtracted
So, the difference of their squares is
And we know that this difference is 68, so the equation is
So, the two consecutive even integers are 16 and 18.
Let's check the answer!
The difference of their squares is