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Surd Problem

  1. Feb 26, 2005 #1
    HELP!!!!! PLease cna someone explain how to do this quck please?!!

    1
    ----- + (root3+1)squared
    root3+1
     
  2. jcsd
  3. Feb 26, 2005 #2
    What are you trying to find?
     
  4. Feb 27, 2005 #3
    [tex]\frac{1}{\sqrt{3}+1}+(\sqrt{3}+1)^2[/tex]
    is I believe what he was trying to get the answer to.

    EDIT: Bah, read below...
     
    Last edited: Feb 27, 2005
  5. Feb 27, 2005 #4
    I got [tex]\frac{5}{2}\sqrt{3}+\frac{7}{2}[/tex]
     
  6. Feb 27, 2005 #5
    What? Wait... d'oh! I forgot to divide the other half of the expression by [tex]\sqrt{3}-1[/tex]... Seems like the whole thing doesn't work now...

    Then you have to go about it like so:

    [tex]\frac{1}{\sqrt{3}+1}+(\sqrt{3}+1)^2[/tex]
    [tex]=\frac{1+(\sqrt{3}+1)^3}{\sqrt{3}+1}[/tex]
    [tex]=\frac{(1+(\sqrt{3}+1)^3)(\sqrt{3}-1)}{(\sqrt{3}+1)(\sqrt{3}-1)}[/tex]
    [tex]=\frac{\sqrt{3}-1+2(\sqrt{3}+1)^2}{2}[/tex]
    [tex]=\frac{\sqrt{3}-1+4\sqrt{3}+8}{2}[/tex]
    [tex]=\frac{5\sqrt{3}+7}{2}[/tex]
    [tex]=\frac{5}{2}\sqrt{3}+\frac{7}{2}[/tex]

    Which is far more correct...
     
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