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Discussion :: Quadratic Equations

  1. The sum of the square of the three consecutive even natural numbers is 1460. Find the numbers?
    2. A.
    18, 20, 22
    B.
    20, 22, 24
    C.
    22, 24, 26
    D.
    24, 26, 28
    E.
    None of these

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    Answer : Option B

    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.

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