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Cubic root equations

  1. Aug 16, 2011 #1
    Hi, can you help me with this problem?

    [itex]a = \sqrt[3]{1 - 4b - 4c}[/itex]
    [itex]b = \sqrt[3]{1 - 4c - 4a}[/itex]
    [itex]c = \sqrt[3]{1 - 4a - 4b}[/itex]

    Find [itex]\dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c}[/itex]

    Thanks
     
  2. jcsd
  3. Aug 16, 2011 #2
    a^3 = 1 -4b -4c
    b^3 = 1- 4c -4a
    c^3 = 1- 4a -4b
    => a^3 +4b +4c = b^3 +4c +4a = c^3 +4a + 4b
    <=> a^3 + 4b + 4c = b^3 + 4c + 4a and a^3 + 4b + 4c = c^3 +4a +4b
    <=> a+b+c = 0 ( I have ignored the conditions a =b or a =c since they are easy)
    it should be easy by replacing a + b + c = 0 into those first equations
     
    Last edited: Aug 16, 2011
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