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This is the first reply email from Fujio KIDA in Japan to CAS on the
attached luigi's email.
I tried and could find three distinct solutions by adding "dummy variable
a=1" as follows;
solve([
0=35*x^3+(35*sqrt(3)-9)*x^2-(9*sqrt(3)+2)*x-2*sqrt(3) ,
a=1
],[ a,x]);
As Mr luigi said, Maxima sometime does not give the answers as we hope.
(I have benefited quite a lot from using Maxima, and much better than
"Mathematica" for my purposes.)
Also, Maxima gave three solutions in complex formula as expected for the
third order polynomials.
Fujio KIDA
???: luigi_marino2 at alice.it
<http://www.math.utexas.edu/mailman/listinfo/maxima>;
??: maxima at math.utexas.edu
<http://www.math.utexas.edu/mailman/listinfo/maxima>;
??: 2011/08/12 16:51
??: [Maxima] solve in Maxima
Maxima cannot exactly solve this polynomial
with not-rational coefficients:
35x^3+(35*sqrt(3)-9)x^2-(9*sqrt(3)+2)x-2*sqrt(3)
the real solutions are:
-sqrt(3) , -1/7 , 2/5
the only method is:
divide(
35x^3+(35*sqrt(3)-9)x^2-(9*sqrt(3)+2)x-2*sqrt(3),x-2/5)
and then
solve(%,x)
Best regards
Luigi Marino_______________________________________________
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(%i1) eq:35*x^3+(35*sqrt(3)-9)*x^2-(9*sqrt(3)+2)*x-2*sqrt(3)=0$
(%i2) factor(eq,a^2-3);
(%o2) (x+sqrt(3))*(5*x-2)*(7*x+1)=0
or
(%i3) gfactor(eq);
(%o3) (x+sqrt(3))*(5*x-2)*(7*x+1)=0
(%i4) solve(%);
(%o4) [x=-1/7,x=2/5,x=-sqrt(3)]
(%i5) build_info()$
Maxima version: 5.25.0
Maxima build date: 12:0 8/2/2011
Host type: i686-pc-mingw32
Lisp implementation type: Clozure Common Lisp
Lisp implementation version: Version 1.7-r14925M (WindowsX8632)
Aleksas D