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Square roots and Quad Form

  1. Mar 31, 2009 #1
    1. Sqrt(x)+1=-2Sqrt(x-3)
    1.) Sqrt(x)=-2Sqrt(x-3)-1 ( )^2 gives

    2.) x= (-2sqrt(x-3)-1)^2 and here I think you need to attempt to foil but im not sure how it works.
    (-2sqrt(x-3)-1)(-2sqrt(x-3)-1)=x

    3.4sqrt(x-3)+2sqrt(x-3)+2sqrt(x-3)+1=x? Not really sure if this is correct



    2. Relevant equations



    3. First step I subtract 1 from ea side, and take the whole equation to the power of ^2.
    I know for the end of the problem I need to summarize like terms to one side and set it =0 and take the quadratic formula to get 2 answers. 1 will be extraneous.
    Any help is greatly appreciated
     
  2. jcsd
  3. Mar 31, 2009 #2

    HallsofIvy

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    Didn't you forget to multiply the squareroots? (That's the "F" in "FOIL".)
    [itex]4(\sqrt{x-3})^2+ 4\sqrt{x-3}+ 1= x[/itex]
    [itex]4(x-3)+ 4\sqrt{x-3}+ 1= x[/itex]
    [itex]4x- 12+ 4\sqrt{x-3}+ 1= x[/itex]
    [itex]4\sqrt{x-3}= -3x+ 7[/itex]
    Now square again to get rid of that square root.





     
  4. Apr 6, 2009 #3
    Ok, I think I understood the original problem correctly.
    Here is how I read it:
    [tex]\sqrt{x}[/tex] + 1= -2[tex]\sqrt{x-3}[/tex]
    First thing I would do is square the entire equation. Giving:
    ([tex]\sqrt{x}[/tex] + 1)[tex]^{2}[/tex] = 4(x-3)
    By using the foil method on the left side of the equation and distributing the 4 on the right, you get:
    x + 2[tex]\sqrt{x}[/tex] + 1 = 4x - 12
    Move the x and the 1 to the right side:
    2[tex]\sqrt{x}[/tex] = 3x - 13
    Now you can square again and get rid of the last square root:
    4x = (3x - 13)[tex]^{2}[/tex]
    Foil that:
    4x = 9x[tex]^{2}[/tex] - 78x + 169
    Move the 4x over:
    0 = 9x[tex]^{2}[/tex] - 82x + 169
    Then you're ready to use the quadratic formula!

    Using the method that you originally attempted would work, but foiling with a square root can get confusing. You always have to square the equation twice to get rid of all of the radicals. For me it is easier to foil a square root when there is not a coefficient in front of it, otherwise I end up forgetting to multiply something along the way. Hope this helps!!!
     
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