Using the fact that, if x represents an even integer, the
[tex]x+2,[/tex]represents the next consecutive even integer, we can set the following equation:
[tex](x+2)^2-x^2=12.[/tex]Simplifying the above equation, we get:
[tex]x^2+4x+4-x^2=12.[/tex]Adding like terms:
[tex]4x+4=12.[/tex]Subtracting 4 from both sides of the equation we get:
[tex]4x=8.[/tex]Dividing by 4, we get:
[tex]x=2.[/tex]Answer:
[tex]2\text{ and 4.}[/tex]