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6 October, 17:01

The difference of the squares of two positive consecutive even integers is 28.

Find the integers. Use the fact that, if x represents an even integer, then x+2 represents the next consecutive even integer.

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  1. 6 October, 19:11
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    If x is the first even integer, then the next is x+2.

    The difference of their squares is (x+2) ^2 - x^2, and this is equal to 28.

    Expanding:

    x^2 + 4x + 4 - x^2 = 28

    4x + 4 = 28

    4x = 24

    x = 6

    x+2 = 8

    Therefore, the two numbers are 6 and 8.
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