Algebra

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Need a formula; the product of two consecutive integers is 41 more than their sum. Find the integers.

  • Algebra -

    let the two numbers be x and x+1

    then x(x+1) = x + y + 41
    expanding and simplifying we get
    x^2 - x - 42 = 0
    (x-7)(x+6) = 0
    x = 7 or x = -6

    case 1: the two numbers are 7 and 8
    check: product = 56
    sum = 15, 56 is greater than 15 by 41

    case 2: the two numbers are -6 and -5
    check: product is 30
    sum is -11
    30 is 41 greater than -11

    so the two numbers are either 7 and 8 or
    -6 and -5

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