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30 January, 16:51

The product of two consecutive positive integers is 812. What is the value of the lesser integer?

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  1. 30 January, 17:03
    0
    lets name the smaller integer as x

    the consecutive integer is x + 1 as its the next number

    the product of these 2 numbers are 812

    you get the product once you multiply the 2 numbers

    x * (x + 1) = 812

    x² + 1x = 812

    x² + x - 812 = 0

    this a quadratic equation

    we have to first find the factors of 812 * x² with a difference or sum of + x

    the 2 factors are + 29x and - 28x which have a product of 812x² and difference of + x

    we substitute + x in the quadratic equation with + 29x - 28x

    x² + 29x - 28x - 812 = 0

    x (x + 29) - 28 (x + 29) = 0

    (x + 29) (x-28) = 0

    so there are 2 possibilites for x

    x + 29 = 0 or x - 28 = 0

    x = - 29 x = 28

    since we are asked to find positive integers from the 2 possible values of x

    x = 28 is the positive number

    therefore smaller integer is 28
  2. 30 January, 17:18
    0
    The answer the question, let x be the smaller positive integer. With this, the greater integer may be represented as x + 1. The product of these integers is 812. The product may be written as,

    (x) (x + 1) = 812

    Solving for x in this problem gives x = 28 or x = - 29. Since we are asked about positive integers only, x = - 29 becomes an extraneous root. Thus, the lesser integer is 28.
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