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29 September, 06:48

Suppose that you have three consecutive positive integers where the product of the smaller and larger number is equal to 15 more than 6 times the middle number. Find the 3 numbers, be sure to include all possibilities.

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  1. 29 September, 08:00
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    The numbers are either {-3, - 2, - 1} or {7, 8, 9}.

    Step-by-step explanation:

    Let the smallest integer be represented by x. The middle number is x+1, and the largest number is x+2.

    The product of the smaller and larger number is (x) (x+2).

    15 more than 6 times the middle number is 6 (x+1) + 15.

    (x) (x+2) = 6 (x+1) + 15

    x^2+2x=6x+6+15

    x^2+2x=6x+21

    x^2-4x-21=0

    (x-7) (x+3) = 0

    x=-3 or x=7

    The numbers are either {-3, - 2, - 1} or {7, 8, 9}.
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