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^33X+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 JeanPierre Escofier Théorie de Galois one can find an exercice for this but not simple

