Question

The sum od the squares of two consecutive even integers is 164. Find the integers.

Answer 1

Let x be the smaller integer, then x+2 is the larger integer.
We're given
x^2+(x+2)^2=164
Expand and simplify
2x^2+4x+4=164
x^2+2x-80=0
(x-8)(x+10)=0
=> x=-10 or x=8.

Therefore the integers are{8,10} or {-10,-8}.
Note: question asks for integers, so negative integers count.