college math

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one number is 8 more than twice another. their product is 8 more than twice their sum. find the numbers

  • college math -

    N1=8+2*N2
    N1*N2=8+2(N1+N2)

  • college math -

    Let the smaller number be x; that means the other number must be 2x + 8.

    Solve the equation
    x(2x+8) = 2x + 8 + x + 8

    which can also be written

    2x^2 + 8x = 3x + 16
    or
    2x^2 + 5x -16 = 0

    There seems to be no integer solution. The smaller number is
    x = (-5 + sqrt 153)/4 = 1.84233
    and the larger number is 2x + 1 = 11.68466
    Their sum is 13.5267
    and the product is 21.527
    as required.

  • college math -

    drwls, you made a slight mistake - you forgot a factor of 2 in the RHS of the equation.

    If N1 = x and N2 = 2x + 8
    then the equation is
    x(2x+8) = 8 + 2*(2x + 8 + x)
    Which simplifies to
    x^2 - x - 12 = 0
    which has two integer solutions.

    Hope that helps!

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