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Math Help - Graphs/equations/point of intersection

  1. #1
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    Graphs/equations/point of intersection

    The solutions of the equation 2x + 2/x = 7 are the x-coordinates of the points of intersection of the graph of y = x + 2/x and a straight line L
    Find the equation of L.
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  2. #2
    No one in Particular VonNemo19's Avatar
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    First find x in the first equation

    2x+\frac{2}{x}=7

    x+\frac{1}{x}=\frac{7}{2}

    \frac{x^2+1}{x}=\frac{7}{2}

    x^2+1=\frac{7}{2}x

    \frac{7}{2}x-\frac{2x^2}{2}=1

    \frac{7x-2x^2}{2}=1

    7x-2x^2=2

    x^2-\frac{7}{2}x=-1

    x^2-\frac{7}{2}x+\frac{49}{16}=1+\frac{49}{16}

    (x-\frac{7}{4})^2=1+\frac{49}{16}

    x-\frac{7}{4}=\pm{\sqrt{1+\frac{49}{16}}}

    x=\pm{\sqrt{1+\frac{49}{16}}}+\frac{7}{4}

    So this particular value of x lies on the graph of the equation y=x+\frac{2}{x} and is also a point on the line L.

    Can you take it from here?

    I'll give you a hint.

    Plug the values +{\sqrt{1+\frac{49}{16}}}+\frac{7}{4} and -{\sqrt{1+\frac{49}{16}}}+\frac{7}{4} into the equation y=x+\frac{2}{x}. They are two points on L.
    Last edited by VonNemo19; May 17th 2009 at 12:44 PM.
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  3. #3
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    2x +2/x = 7
    subtract x from both sides
    x + 2/x = 7 - x

    so you need to draw y = x + 2/x and the straight line y = 7 - x

    It's as simple as that!!
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  4. #4
    No one in Particular VonNemo19's Avatar
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    yes
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