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Homework Help: Rationalize the denominator

  1. Jul 21, 2010 #1
    1. The problem statement, all variables and given/known data
    Rationalize the denominator..
    [tex]
    \frac{1}{\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}}
    [/tex]


    2. Relevant equations

    Algebraic equations.

    3. The attempt at a solution
    So using the form
    a3 + b3 + c3 - 3abc= (a + b + c)(a2 + b2 + c2 - ab - bc - ca)

    So it becomes


    [tex]
    \frac{\sqrt[3]{a^2}+\sqrt[3]{b^2}+\sqrt[3]{c^2} -\sqrt[3]{ab}-\sqrt[3]{bc}-\sqrt[3]{ca} }{a + b + c - 3 \sqrt[3]{abc}}
    [/tex]


    Actually I dunno what to do next
    If i try (a+b)(a-b) then it doesnt work out ...
     
  2. jcsd
  3. Jul 21, 2010 #2

    ehild

    User Avatar
    Homework Helper

    Re: Rationalize!!

    Use

    [tex]x^3-y^3=(x-y)(x^2+xy+y^2)[/tex]

    ehild
     
  4. Jul 21, 2010 #3

    Mark44

    Staff: Mentor

    Re: Rationalize!!

    I don't see how this applies to the OP's problem.
     
  5. Jul 21, 2010 #4

    Mentallic

    User Avatar
    Homework Helper

    Re: Rationalize!!

    [tex]x-y=\frac{x^3-y^3}{x^2+xy+y^2}[/tex]

    :wink:
     
  6. Jul 21, 2010 #5

    Mark44

    Staff: Mentor

    Re: Rationalize!!

    Good thing you put in the wink emoticon.
     
  7. Jul 21, 2010 #6

    Mentallic

    User Avatar
    Homework Helper

    Re: Rationalize!!

    Of course! An emoticon is worth a thousands words.

    If there were a more suitable emoticon for "I'm sure you get it now" I would use that one instead.

    :smile: << (don't kill me for this :tongue:)
     
  8. Jul 25, 2010 #7
    Re: Rationalize!!

    Yup got it!
    Thanks!

    (Checked it out with my teacher ... its right!!)
     
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