Sorry that Maxima doesn't do a better job here. But...
expr: 35*x^3+(35*sqrt(3)-9)*x^2-(9*sqrt(3)+2)*x-2*sqrt(3)$
(Note the use of "*" for multiplication)
solve(expr,x) returns three very messy solutions. Though these are correct,
they are very difficult to simplify to anything more usable.
On the other hand,
gfactor(expr)
returns (x+sqrt(3))*(5*x-2)*(7*x+1)
which solve, of course, easily solves:
[x = -1/7,x = 2/5,x = -sqrt(3)]
Presumably solve should be using gfactor rather than (real) factor.
-s
On Thu, Aug 11, 2011 at 04:14, Luigi Marino <luigi_marino2 at alice.it> wrote:
> **
> Maxima cannot exactly solve this polynomial
> with not-rational coefficients:
>
> 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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