What is the sum of two consecutive even numbers, the difference of whose squares is 84? · ABC26GN1723

Let the numbers be $x$ and $x+2$. Then, $(x+2)^{2}-x^{2}=84$ $$\begin{array}{ll} \Leftrightarrow & 4 x+4=84 \\ \Leftrightarrow & 4 x=80 \\ \Leftrightarrow & x=20 . \\ \therefore & \text { Required sum }=x+(x+2)=2 x+2=42 . \end{array}$$