# What two consecutive even integers sum of squares is 340?

The sum of squares of two consecutive even integers is 340. What are these two consecutive even numbers? The answer is 12 and 14. You must be interested in how to find these two consecutive even integers whose sum of squares is 340. 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 340. The specific steps are as follows:

• 1Enter 340 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 12 and 14, and the other set is -14 and -12.

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 340, which can be expressed by the equation

(2 * N)2 + (2 * N + 2)2 = 340

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 = 340

4 * N2 + 4 * N2 + 8 * N + 4 = 340

8 * N2 + 8 * N + 4 = 340

8 * N2 + 8 * N + 4 – 340 = 0

8 * N2 + 8 * N – 336 = 0

N2 + N – 42 = 0

(N – 6) * (N + 7) = 0

N = 6 or N = -7

So, 2 * N = 12 or -14

So, the value of the first even integer is 12 or -14, then the second even integer is 14 or -12.

Obviously, there are 2 sets of answers for which the sum of the squares of two consecutive even numbers is 340. The positive even integers are 12 and 14, the negative even integers are -14 and -12. 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 340 / 2 = 170.

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

Here it is √170.0 = 13.0384.

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

In here, find 2 consecutive even integers around 13.0384, and their average value is equal to 13.0384.

Through the above 3 steps, you can find that these 2 consecutive even integers are 12 and 14.

Let us verify that the answer is correct?

122 + 142 = 144 + 196 = 340

Next, we consider the negative forms of these two even integers -14 and -12, and we can get another answer.

## Problems can be solved by two consecutive even integers whose sum of squares is 340

Now, we have found 2 consecutive even integers whose sum of squares is 340. At the same time, the following problems can also be solved incidentally.

• 1The sum of squares of two consecutive even integers is 340, and their sum is 12 + 14 = 26.
• 2The sum of squares of two consecutive even integers is 340, and their product is 12 * 14 = 168.
• 3The sum of squares of two consecutive even integers is 340, and the sum of their cubes is 123 + 143 = 4472.
• 4The sum of squares of two consecutive even integers is 340, and the smaller positive integer is 12.
• 5The sum of squares of two consecutive even integers is 340, and the larger positive integer is 14.
• 6The sum of squares of two consecutive even integers is 340, and their average is 13.

Of course, in addition to the three methods described above for finding two consecutive even integers whose sum of squares is 340, there are other methods. Have you encountered them? If so, please leave a message to tell us, thank you!

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