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

Quadratic Equations 03/05/2020

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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