##### Calculate the average of the sum of squares first.

That is, divide the sum of squares by the number. Here it is 113 / 2 = 56.5.

The sum of squares of two consecutive integers is 113. What are these two consecutive numbers? **The answer is 7 and 8.** You must be interested in ** how to find these two consecutive integers whose sum of squares is 113**. Here will introduce a calculator and 2 methods to solve this problem. The calculator is suitable for everyone, including laymen. Two methods are suitable for those who have some foundation in mathematics. let’s start.

With the help of the above calculator, we can easily find 2 consecutive integers whose sum of squares is 113. The specific steps are as follows:

- Enter 113 into the input box.
- Click the calculation button.

In the blink of an eye, the answer will appear. As shown in the figure, there are two sets of answers, one set is 7 and 8, and the other set is -8 and -7.

Very simple, if you have other similar problems: **find 2 consecutive integers based on the sum of squares**. It can be calculated by the sum-squares-based 2 consecutive integers calculator.

Assuming that **N** is used to represent the first integer, then the second integer can be represented by **N + 1**. Now, the sum of squares of 2 consecutive integers is 113, which can be expressed by the equation

N

^{2}+ (N + 1)^{2}= 113

This is a quadratic equation in one variable. When we solve this equation, we can get the value of the first integer **N**.

N

^{2}+ (N + 1)^{2}= 113N

^{2}+ N^{2}+ 2 * N + 1 = 1132 * N

^{2}+ 2 * N + 1 = 1132 * N

^{2}+ 2 * N + 1 – 113 = 02 * N

^{2}+ 2 * N – 112 = 0N

^{2}+ N – 56 = 0(N – 7) * (N + 8) = 0

N = 7 or N = -8

So, the value of the first integer is 7 or -8, then the second integer is **N + 1 = 8 or -7**.

Obviously, there are 2 sets of answers for which the sum of the squares of two consecutive numbers is 113. The positive integers are 7 and 8, the negative integers are -8 and -7. It is consistent with the answer calculated by the calculator in the first method!

1

That is, divide the sum of squares by the number. Here it is 113 / 2 = 56.5.

2

Here it is √56.5 = 7.5.

3

In here, find 2 consecutive integers around 7.5, and their average value is equal to 7.5.

Through the above 3 steps, you can find that these 2 consecutive integers are 7 and 8.

Let us verify that the answer is correct?

7

^{2}+ 8^{2}= 49 + 64 = 113

Obviously, this answer is correct.

Next, we consider the negative forms of these two integers -7 and -8, and we can get another answer.

Now, we have found 2 consecutive integers whose sum of squares is 113. At the same time, the following problems can also be solved incidentally.

- The sum of squares of two consecutive integers is 113, and their sum is 7 + 8 = 15.
- The sum of squares of two consecutive integers is 113, and their product is 7 * 8 = 56.
- The sum of squares of two consecutive integers is 113, and the sum of their cubes is 7
^{3}+ 8^{3}= 855. - The sum of squares of two consecutive integers is 113, and the smaller positive integer is 7.
- The sum of squares of two consecutive integers is 113, and the larger positive integer is 8.
- The sum of squares of two consecutive integers is 113, and their average is 7.5.

Of course, in addition to the three methods described above for finding two consecutive integers whose sum of squares is 113, there are other methods. Have you encountered them? If so, please leave a message to tell us, thank you!

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