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18 September, 14:37

The product of two consecutive integers is equal to 14 more than 4 times the sum. This can be simplified to x²-7x-18=0. What are the two integers?

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  1. 18 September, 14:55
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    -1 and - 2, or 9 and 10

    Step-by-step explanation:

    If x is the smaller integer:

    x (x + 1) = 14 + 4 (x + x + 1)

    x² + x = 14 + 4 (2x + 1)

    x² + x = 14 + 8x + 4

    x² - 7x - 18 = 0

    Factor using AC method:

    (x - 9) (x + 2) = 0

    x = - 2 or 9

    x is the smaller integer, so the larger integers are - 1 and 10. Check each pair of solutions.

    -1 and - 2:

    (-2) (-1) = 14 + 4 (-2 + - 1)

    2 = 14 + 4 (-3)

    2 = 2

    9 and 10:

    (9) (10) = 14 + 4 (9 + 10)

    90 = 14 + 4 (19)

    90 = 90

    Both solutions work.
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