Question
The sum of the square of the three consecutive even natural numbers is 1460. Find the numbers?
Answer: Option B
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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.
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