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Math Help - solutions to an equation question

  1. #1
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    solutions to an equation question

    (x-3)^(1/2) - (x)^(1/2) = -3

    How many solutions, if any are in this equation? I can't seem to be able to factor this :S Any suggestions are greatly appreciated!
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  2. #2
    o_O
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    \begin{array}{rcl} \sqrt{x-3} - \sqrt{x} & = & - 3 \\ \sqrt{x - 3} & = &  \sqrt{x} - 3 \\ x - 3 & = & x - 6\sqrt{x} + 9 \qquad \text{Squared both sides} \\ 6\sqrt{x} & = & 12 \\ & \vdots & \end{array}

    What can you concude?
    Last edited by o_O; September 19th 2008 at 06:38 PM.
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  3. #3
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    Hello, finalfantasy!

    \sqrt{x-3}  - \sqrt{x} \;=\; -3

    How many solutions, if any, are in this equation?[
    Why are you trying to factor?


    We have:

    . \sqrt{x-3} \;=\;\sqrt{x} - 3

    Square both sides:

    . . x - 3 \;=\;x - 6\sqrt{x} + 9

    . . . 6\sqrt{x} \;=\;12

    . . . \sqrt{x} \;=\;2

    . . . . x \;=\;4\quad\hdots . but this root is extraneous


    There are no solutions.

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