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Homework Help: Solving equation with cube roots.

  1. Jun 24, 2012 #1
    1. The problem statement, all variables and given/known data
    Solve the equation:


    3. The attempt at a solution

    What I did was move (x+3)^(1/3) to the other side, cube both sides and when I put them equal to 0 again, I managed to factor (x+2)^(1/3) out of it giving one solution x=-2.

    However if I looked up the proposed solution after cubing and a little gathering and grouping it arrived at this:


    Which is clear, but then in the next step it is converted to this without explanation:


    From there on the solution is just putting it equal to 0 and factorizing, but how did it get to this from the previous? It would imply [itex]-(\sqrt[3]{x+1}+\sqrt[3]{x+2})[/itex] is equal to [itex]\sqrt[3]{(x+3)}[/itex], which I don't think it is. Is it wrong or what is up with that?
  2. jcsd
  3. Jun 24, 2012 #2


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    Science Advisor

    Look at your original equation:
    This means:
    Plug this into:
    and cancel out a factor of 3 to give:
  4. Jun 24, 2012 #3
    Oh, didn't see that, thank you.
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