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2 October, 04:08

The square of the sum of two consecutive positive even integers is 4048 more than the sum of the squares of these two numbers. Find the two numbers.

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  1. 2 October, 05:53
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    44 and 46.

    Step-by-step explanation:

    Let the 2 numbers be x and x + 2 (because they are consecutive even numbers). So:

    (x + (x + 2)) ^2 = 4048 + x^2 + (x + 2) ^2

    (2x + 2) ^2 - x^2 - (x + 2) ^2 = 4048

    4x^2 + 8x + 4 - x^2 - (x^2 + 4x + 4) = 4048

    4x^2 - x^2 - x^2 + 8x - 4x + 4 - 4 = 4048

    2x^2 + 4x - 4048 = 0

    x^2 + 2x - 2024 = 0

    (x - 44) (x + 46) = 0

    x = 44 because we are given that it is positive.

    Therefore the other number is x + 2 = 46.
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