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Homework Help: Algebra radicals problem

  1. Sep 5, 2011 #1
    1. The problem statement, all variables and given/known data

    This is the problem. I seem to be having a hard time removing the radicals.
    The answer should be 12/5. I have no idea how to get there. I am just trying to learn how to handle a situation like this, so I can be prepared in the future.

    2x*(4x-1)^-1/2 - 3sqrt(4-x) = 0

    3. The attempt at a solution

    I've tried flipping the negative exponent into a fraction and then combining it into one fraction. I tried to directly remove the radicals by squaring everything, but somewhere I must be doing something wrong.

    Any hints to the procedures on how to solve this?
  2. jcsd
  3. Sep 6, 2011 #2


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    Add [itex]3(\sqrt{4-x}\,)[/itex] to both sides.

    Multiply both sides by [itex]\sqrt{4x-1}\,.[/itex]

    Square both sides.

    After doing some algebra, you will have a quadratic equation
  4. Sep 6, 2011 #3


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    2x*(4x-1)^-1/2 - 3sqrt(4-x) = 0

    [itex]\frac{2x}{\sqrt{4x-1}} - 3\sqrt{4-x}=0[/itex]
    [itex]\frac{2x}{\sqrt{4x-1}} = 3\sqrt{4-x}[/itex]
    Square both sides.
  5. Sep 11, 2011 #4
    Just replying to thank you for your swift response! Much appreciated. Yes, that did help me quite a bit. In the future, I will be including more info on how I approached the problem. I was really tired that night.
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