# The square of the sum of two consecutive integers is 1681. What are the integers?

##### 1 Answer

20 and 21.

#### Explanation:

Let's say the two consecutive numbers are

"The square of the sum of two consecutive integers is

Now, there are two variables here so at first glance it looks unsolvable. But we're also told that

Substituting this new information in gives us:

Next we're going to follow these steps to solve for

1) Take the square root of both sides. This will give two possible results, since both positive and negative numbers have positive squares.

2) Subtract

3) Divide both sides by

4) Check the answer.

This means that

Success!