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

 Messages: [ Previous | Next ]
 AP Posts: 137 Registered: 3/4/09
Re: Cubics and roots
Posted: Oct 16, 2012 10:44 AM

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?
>
>quasi

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

Date Subject Author
10/14/12 Bill Taylor
10/15/12 William Elliot
10/15/12 Frederick Williams
10/15/12 William Elliot
10/16/12 Frederick Williams
10/16/12 Pubkeybreaker
10/15/12 Robin Chapman
10/16/12 AP
10/16/12 quasi
10/16/12 AP
10/16/12 quasi
10/18/12 AP
10/18/12 quasi
10/18/12 AP
10/18/12 quasi
10/19/12 quasi
10/18/12 Dave L. Renfro
10/19/12 quasi
10/19/12 quasi
10/15/12 quasi
10/16/12 Bill Taylor
10/16/12 quasi
10/16/12 quasi
10/19/12 quasi
10/18/12 James Bryce