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Math Help - Help!

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    21

    Help!

    Can someone show me how to manipulate the following, in stages, to find x:

    x = \frac{4(\sqrt2 - 1) \pm \sqrt{(4(\sqrt2 - 1))^2 + 4(1)(29+8\sqrt2)}}{2}
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  2. #2
    Senior Member
    Joined
    Dec 2007
    From
    Anchorage, AK
    Posts
    276
    First, you can factor out 4 from the term in the large root:
    x=\frac{4(\sqrt{2}-1)\pm\sqrt{4(4(\sqrt{2}-1)^2+29+8\sqrt{2})}}{2}
    x=\frac{4(\sqrt{2}-1)\pm{2}\sqrt{(4(\sqrt{2}-1)^2+29+8\sqrt{2})}}{2}
    x=2(\sqrt{2}-1)\pm\sqrt{4(\sqrt{2}-1)^2+29+8\sqrt{2}}.

    Next, use that
    (\sqrt{2}-1)^2=(\sqrt{2})^2-2(1)\sqrt{2}+1^2
    \;\;=2-2\sqrt{2}+1
    \;\;=3-2\sqrt{2}

    So:
    x=2(\sqrt{2}-1)\pm\sqrt{4(3-2\sqrt{2})+29+8\sqrt{2}}
    x=2(\sqrt{2}-1)\pm\sqrt{12-8\sqrt{2}+29+8\sqrt{2}}
    x=2(\sqrt{2}-1)\pm\sqrt{41}

    -Kevin C.
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