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Topic: Cubics and roots
Replies: 24   Last Post: Oct 19, 2012 4:15 PM

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Posts: 137
Registered: 3/4/09
Re: Cubics and roots
Posted: Oct 16, 2012 10:44 AM
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On Tue, 16 Oct 2012 07:18:35 -0500, quasi <quasi@null.set> wrote:

>AP wrote:
>>P=X^3-3X+1 is irreducible on Q
>>his roots are 2cos(pi/9) ; 2cos(7pi/9) ; 2cos(5pi/9)
>>not obtainable via the four basic operations and
>>squre, cube,.. roots of positifs numbers.

>The cubic formula expresses those roots using imaginary
>numbers, but how can you _prove_ that there is no way
>to express those roots using only real square roots, real
>cube roots, and the usual arithmetic operations?

in the book of Jean-Pierre Escofier
Théorie de Galois
one can find an exercice for this
but not simple

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