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the product of three consecutive integers is 22 less than the cube of the middle integer. Find the integer.

  • math -

    let the 3 consecutive integers be
    x-1, x, and x+1

    ( I wanted to cube x , not x+1 )

    x(x-1)(x+1) = x^3 - 22
    x^3 - x = x^3 - 22
    x = 22

    the 3 integers are 21 , 22, and 23

    check: product of 3 numbers = 21x22x23 = 10626
    cube of 22 = 10648
    is the product 22 less than the cube? YES

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