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Math Help - Need quick help with equation

  1. #1
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    Need quick help with equation

    1.Two one by one natural numbers sum 109 is smaller then there product.Find those numbers.
    {y=x+1
    xy=x+y+109

    x=y-1
    (y-1)y=x+y+109 Whats next?

    2. Right-angled parterres area is 56m2(square),and the fence,that surrounds the parterre is 30m.Find the parterres dimension.


    Please someone help.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Neurok View Post
    1.Two one by one natural numbers sum 109 is smaller then there product.Find those numbers.
    {y=x+1
    xy=x+y+109

    x=y-1
    (y-1)y=x+y+109 Whats next?
    I'm going to assume you set up the problem correctly because I can't make sense out of the question.

    First you need to replace ALL x's in the second equation:
    xy = x + y + 109

    (y - 1)y = (y - 1) + y + 109

    y^2 - y = 2y + 108

    y^2 - 3y - 108 = 0

    (y - 12)(y + 9) = 0

    Thus y = 12 or y = -9. This means that x = 11 or x = -10 respectively.

    So your solutions are: (x, y) = (11, 12) or (x, y) = (-10, -9).

    -Dan
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Neurok View Post
    2. Right-angled parterres area is 56m2(square),and the fence,that surrounds the parterre is 30m.Find the parterres dimension.
    I'm assuming your parterre is a rectangle, rather than a square. So let the dimensions of the parterre be x and y. The we know that
    xy = 56
    2x + 2y = 30

    From the second equation:
    2x + 2y = 30

    x + y = 15

    y = 15 - x

    Inserting this into the first equation gives:
    xy = 56

    x(15 - x) = 56

    15x - x^2 = 56

    x^2 - 15x + 56 = 0

    (x - 7)(x - 8) = 0

    So x = 7 m or x = 8 m. Thus y = 8 m or y = 7 m respectively. Either way the dimensions of the parterre are 7 m by 8 m.

    -Dan
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    Thank you.
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