The sum of the square of the three consecutive even natural numbers is 1460. Find the numbers?

A. 18, 20, 22
B. 20, 22, 24
C. 22, 24, 26
D. 24, 26, 28

Explanation:

Three consecutive even natural numbers be 2x – 2, 2x and 2x + 2.
(2x – 2)2 + (2x)2 + (2x + 2)2 = 1460
4×2 – 8x + 4 + 4×2 + 8x + 4 = 1460
12×2 = 1452 => x2 = 121 => x = ± 11
As the numbers are positive, 2x > 0. Hence x > 0. Hence x = 11.
Required numbers are 20, 22, 24.

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