# What two consecutive integers sum of squares is 925?

The sum of squares of two consecutive integers is 925. What are these two consecutive numbers? The answer is 21 and 22. You must be interested in how to find these two consecutive integers whose sum of squares is 925. 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.

## 1. Sum-Squares-Based 2 Consecutive Integers Calculator

Result:
Verify:

With the help of the above calculator, we can easily find 2 consecutive integers whose sum of squares is 925. The specific steps are as follows:

• 1Enter 925 into the input box.
• 2Click 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 21 and 22, and the other set is -22 and -21.

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 or more advanced sum squares based consecutive integers calculator.

## 2. Hypothetical method

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 925, which can be expressed by the equation

N2 + (N + 1)2 = 925

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

N2 + (N + 1)2 = 925

N2 + N2 + 2 * N + 1 = 925

2 * N2 + 2 * N + 1 = 925

2 * N2 + 2 * N + 1 – 925 = 0

2 * N2 + 2 * N – 924 = 0

N2 + N – 462 = 0

(N – 21) * (N + 22) = 0

N = 21 or N = -22

So, the value of the first integer is 21 or -22, then the second integer is N + 1 = 22 or -21.

Obviously, there are 2 sets of answers for which the sum of the squares of two consecutive numbers is 925. The positive integers are 21 and 22, the negative integers are -22 and -21. It is consistent with the answer calculated by the calculator in the first method!

## 3. Average method

1
##### Calculate the average of the sum of squares first.

That is, divide the sum of squares by the number. Here it is 925 / 2 = 462.5.

2
##### Then calculate the square root of the average.

Here it is √462.5 = 21.494.

3
##### Finally, find consecutive integers near the square root value.

In here, find 2 consecutive integers around 21.494, and their average value is equal to 21.494.

Through the above 3 steps, you can find that these 2 consecutive integers are 21 and 22.

Let us verify that the answer is correct?

212 + 222 = 441 + 484 = 925

Next, we consider the negative forms of these two integers -22 and -21, and we can get another answer.

## Problems can be solved by two consecutive integers whose sum of squares is 925

Now, we have found 2 consecutive integers whose sum of squares is 925. At the same time, the following problems can also be solved incidentally.

• 1The sum of squares of two consecutive integers is 925, and their sum is 21 + 22 = 43.
• 2The sum of squares of two consecutive integers is 925, and their product is 21 * 22 = 462.
• 3The sum of squares of two consecutive integers is 925, and the sum of their cubes is 213 + 223 = 19909.
• 4The sum of squares of two consecutive integers is 925, and the smaller positive integer is 21.
• 5The sum of squares of two consecutive integers is 925, and the larger positive integer is 22.
• 6The sum of squares of two consecutive integers is 925, and their average is 21.5.

Of course, in addition to the three methods described above for finding two consecutive integers whose sum of squares is 925, there are other methods. Have you encountered them? If so, please leave a message to tell us, thank you!

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