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Math Help - Number in Q

  1. #1
    Super Member dhiab's Avatar
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    Number in Q

    prouve :
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  2. #2
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    Quote Originally Posted by dhiab View Post
    prouve :

    Hi

    If you consider the equation x^3+5x-6=0 you can find that x=1 is the only real solution since x^3+5x-6=(x-1)(x^2+x+6)

    Now if you try to solve it using Cardan method Méthode de Cardan - Wikipédia you will find that one real solution is

    \sqrt[3]{3+\sqrt{9+\frac{125}{27}}}-\sqrt[3]{-3+\sqrt{9+\frac{125}{27}}}

    Since 1 is the only real solution you get \sqrt[3]{3+\sqrt{9+\frac{125}{27}}}-\sqrt[3]{-3+\sqrt{9+\frac{125}{27}}} = 1
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