Question

The sum of the squares of two consecutive even natural numbers are 724. Find the numbers.
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Answer 1

Given - The sum of the squares of two consecutive even natural numbers are 724

Find - Two consecutive even natural numbers

Solution - Let the two consecutive even natural numbers be x and (x+2). Now expressing the given information in mathematical form-

x² + (x+2)² = 724

Expanding the expression to find the value of x.

x² + x² + 4 + 4x = 724

2x² + 4x + 4 - 724 = 0

2x² + 4x - 720

x² + 2x - 360

x² + 20x - 18x -360

x (x + 20) - 18 ( x + 20)

(x - 18) (x + 20)

Thus, values of x are 18 and -20.

Since natural number can not be negative, thus, value of x will be 18.

Now, the numbers are x and x+2.

Hence, natural numbers = 18 and 18 + 2

Natural numbers = 18 and 20.

Therefore, two consecutive even natural numbers are 18 and 20.

Answer 2

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