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

Quantitative Aptitude (Pb Patwari) Algebra

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

18, 20, 22

20, 22, 24

22, 24, 26

24, 26, 28

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Explanation:

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