Find two consecutive even numbers whose squares differ by 684.

Consecutive even numbers differ from each other by 2 units. This is because these numbers are in the number row one odd number apart.

Let one even number be x, then the second number will be (x + 2). It is known that the difference of the squares of these numbers is equal to (x + 2) ^ 2 – x ^ 2 or 684. Let’s compose an equation and solve it.

(x + 2) ^ 2 – x ^ 2 = 684;

x ^ 2 + 4x + 4 – x ^ 2 = 684;

4x + 4 = 684;

4x = 684 – 4;

4x = 680;

x = 680: 4;

x = 170 – first number;

x + 2 = 170 + 2 = 172 is the second number.

Answer. 170; 172.