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7 April, 20:15

The product of two, positive, consecutive integers is equal to 72. Find both internet's using an algebraic method.

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  1. 7 April, 20:38
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    8 and 9

    Step-by-step explanation:

    From the question we are given;

    The product of two positive consecutive number is 72

    We are required to determine the integers;

    We need to know that the difference between two consecutive integers is 1 Therefore;

    Assuming that the smaller integer is x

    Then the other integer is x+1

    Therefore;

    x (x+1) = 72

    x² + x = 72

    Rearranging in quadratic manner;

    x² + x - 72 = 0

    Solving quadratically, using factor method;

    Product = - 72x

    Sum = x

    Numbers = 9x and - 8x

    Thus;

    x² + 9x - 8x - 72 = 0

    x (x+9) - 8 (x+9) = 0

    Then;

    (x-8) (x+9) = 0

    Hence, x-8 = 0 or x+9 = 0

    Therefore, x = 8 or x = - 9

    We take, x = 8 (positive integer)

    Hence, the required integers are 8 and 9
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