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Math Help - how does this work?

  1. #1
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    how does this work?

    I know that

    1+√5 = 3√(2+√5) = 1.618033989
    2


    but what is the math behind it specifically a way to simplify
    3√(2+√5) to 1+√5

    2


    Thanks


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  2. #2
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    Just to make this clear its (1+√5)/2 which equals 3√(2+√5) I hope that is clear.
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  3. #3
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    Hello,
    Quote Originally Posted by Smoriginal View Post
    Just to make this clear its (1+√5)/2 which equals 3√(2+√5) I hope that is clear.
    \frac{1+\sqrt{5}}{2}=\sqrt[3]{2+\sqrt{5}}

    You can prove it by cubing both sides. This is all I can see for the moment...

    (note : (a+b)^3=a^3+b^3+3ab^2+3a^2b)
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