# What two consecutive odd integers sum of squares is 74?

The sum of squares of two consecutive odd integers is 74. What are these two consecutive odd numbers? The answer is 5 and 7. You must be interested in how to find these two consecutive odd integers whose sum of squares is 74. 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 Odd Integers Calculator

Result:
Verify:

With the help of the above calculator, we can easily find 2 consecutive odd integers whose sum of squares is 74. The specific steps are as follows:

• 1Enter 74 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 5 and 7, and the other set is -7 and -5.

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

## 2. Hypothetical method

Assuming that 2 * N + 1 is used to represent the first odd integer, then the second odd integer can be represented by 2 * N + 3. Now, the sum of squares of 2 consecutive odd integers is 74, which can be expressed by the equation

(2 * N + 1)2 + (2 * N + 3)2 = 74

This is a quadratic equation in one variable. When we solve this equation, we can get the value of the first integer 2 * N + 1.

(2 * N + 1)2 + (2 * N + 3)2 = 74

4 * N2 + 4 * N +1 + 4 * N2 + 12 * N + 9 = 74

8 * N2 + 16 * N + 10 = 74

8 * N2 + 16 * N + 10 – 74 = 0

8 * N2 + 16 * N – 64 = 0

N2 + 2 * N – 8 = 0

(N – 2) * (N + 4) = 0

N = 2 or N = -4

So, 2 * N + 1 = 5 or -7

So, the value of the first odd integer is 5 or -7, then the second odd integer is 7 or -5.

Obviously, there are 2 sets of answers for which the sum of the squares of two consecutive odd numbers is 74. The positive odd integers are 5 and 7, the negative odd integers are -7 and -5. 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 74 / 2 = 37.

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

Here it is √37.0 = 6.08.

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

In here, find 2 consecutive odd integers around 6.08, and their average value is equal to 6.08.

Through the above 3 steps, you can find that these 2 consecutive odd integers are 5 and 7.

Let us verify that the answer is correct?

52 + 72 = 25 + 49 = 74

Next, we consider the negative forms of these two odd integers -7 and -5, and we can get another answer.

## Problems can be solved by two consecutive odd integers whose sum of squares is 74

Now, we have found 2 consecutive odd integers whose sum of squares is 74. At the same time, the following problems can also be solved incidentally.

• 1The sum of squares of two consecutive odd integers is 74, and their sum is 5 + 7 = 12.
• 2The sum of squares of two consecutive odd integers is 74, and their product is 5 * 7 = 35.
• 3The sum of squares of two consecutive odd integers is 74, and the sum of their cubes is 53 + 73 = 468.
• 4The sum of squares of two consecutive odd integers is 74, and the smaller positive integer is 5.
• 5The sum of squares of two consecutive odd integers is 74, and the larger positive integer is 7.
• 6The sum of squares of two consecutive odd integers is 74, and their average is 6.

Of course, in addition to the three methods described above for finding two consecutive odd integers whose sum of squares is 74, there are other methods. Have you encountered them? If so, please leave a message to tell us, thank you!

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