What two consecutive even integers sum of squares is 164?

The sum of squares of two consecutive even integers is 164. What are these two consecutive even numbers? The answer is 8 and 10. You must be interested in how to find these two consecutive even integers whose sum of squares is 164. 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 Even Integers Calculator

Result:
Verify:

With the help of the above calculator, we can easily find 2 consecutive even integers whose sum of squares is 164. The specific steps are as follows:

  • 1Enter 164 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 8 and 10, and the other set is -10 and -8.

What two consecutive even integers sum of squares is 164

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

2. Hypothetical method

Assuming that 2 * N is used to represent the first even integer, then the second even integer can be represented by 2 * N + 2. Now, the sum of squares of 2 consecutive even integers is 164, which can be expressed by the equation

(2 * N)2 + (2 * N + 2)2 = 164

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

(2 * N)2 + (2 * N + 2)2 = 164

4 * N2 + 4 * N2 + 8 * N + 4 = 164

8 * N2 + 8 * N + 4 = 164

8 * N2 + 8 * N + 4 – 164 = 0

8 * N2 + 8 * N – 160 = 0

N2 + N – 20 = 0

(N – 4) * (N + 5) = 0

N = 4 or N = -5

So, 2 * N = 8 or -10

So, the value of the first even integer is 8 or -10, then the second even integer is 2 * N + 2 = 10 or -8.

Obviously, there are 2 sets of answers for which the sum of the squares of two consecutive even numbers is 164. The positive even integers are 8 and 10, the negative even integers are -10 and -8. 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 164 / 2 = 82.

2
Then calculate the square root of the average.

Here it is √82.0 = 9.055.

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

In here, find 2 consecutive even integers around 9.055, and their average value is equal to 9.055.

Through the above 3 steps, you can find that these 2 consecutive even integers are 8 and 10.

Let us verify that the answer is correct?

82 + 102 = 64 + 100 = 164

Obviously, this answer is correct.

Next, we consider the negative forms of these two even integers -10 and -8, and we can get another answer.

Problems can be solved by two consecutive even integers whose sum of squares is 164

Now, we have found 2 consecutive even integers whose sum of squares is 164. At the same time, the following problems can also be solved incidentally.

  • 1The sum of squares of two consecutive even integers is 164, and their sum is 8 + 10 = 18.
  • 2The sum of squares of two consecutive even integers is 164, and their product is 8 * 10 = 80.
  • 3The sum of squares of two consecutive even integers is 164, and the sum of their cubes is 83 + 103 = 1512.
  • 4The sum of squares of two consecutive even integers is 164, and the smaller positive integer is 8.
  • 5The sum of squares of two consecutive even integers is 164, and the larger positive integer is 10.
  • 6The sum of squares of two consecutive even integers is 164, and their average is 9.

Of course, in addition to the three methods described above for finding two consecutive even integers whose sum of squares is 164, there are other methods. Have you encountered them? If so, please leave a message to tell us, thank you!

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