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15 January, 22:08

The difference of the squares of two positive consecutive even integers is 20. find the integers. use the fact that, if x represents an even integer, then xplus 2 represents the next consecutive even integer.

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  1. 15 January, 23:39
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    If x is the first number, x+2 is the next consecutive even integer. The difference (subtraction) of their squares equals 20. Therefore:

    (x+2) ²-x²=20 ... expand this:

    x²+4x+4-x²=20

    x²+4x+4-x²=20

    4x+4=20

    4x=16

    x=4. Therefore the next consecutive even integer is x+2=6.

    To check: 6²-4² must equal 20

    36-16=20 check!
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