what is the sum of two consecutive even numbers, the difference of whose squares is 84?

Let the two consecutive even numbers be xxx and x+2x+2x+2. Their squares are x2x^2x2 and (x+2)2(x+2)^2(x+2)2.
We are told that the difference of their squares is 84, so:

(x+2)2−x2=84(x+2)^2-x^2=84(x+2)2−x2=84

Expand:

(x2+4x+4)−x2=84(x^2+4x+4)-x^2=84(x2+4x+4)−x2=84

4x+4=844x+4=844x+4=84

Solve for xxx:

4x=80⇒x=204x=80\Rightarrow x=204x=80⇒x=20

So the numbers are 20 and 22, and their sum is:

20+22=4220+22=4220+22=42

Answer: 42