On 10/13/2013 09:35 PM, Aleksas Domarkas wrote:
> On 13 Oct 2013 06:19:46 Joerg Rauh wrote:
> > Dear Maxima Supporter,
> > out of wxMaxima 12.04.0 I had Maxima solve for x:
> > ((40-3*x)*(20-2*x)*x)/2-500
> > Here are the results:
> >
[x=(-(sqrt(3)*%i)/2-1/2)*((250*sqrt(101)*%i)/3^(7/2)+25750/729)^(1/3)+(1300*((sqrt(3)*%i)/2-1/2))/(81*((250*sqrt(101)*%i)/3^(7/2)+25750/729)^(1/3))+70/9,
> >
x=((sqrt(3)*%i)/2-1/2)*((250*sqrt(101)*%i)/3^(7/2)+25750/729)^(1/3)+(1300*(-(sqrt(3)*%i)/2-1/2))/(81*((250*sqrt(101)*%i)/3^(7/2)+25750/729)^(1/3))+70/9,
> >
x=((250*sqrt(101)*%i)/3^(7/2)+25750/729)^(1/3)+1300/(81*((250*sqrt(101)*%i)/3^(7/2)+25750/729)^(1/3))
>
> > It missed the real results: x=1.7407 and x=6.23415, which I found here:
>
http://www.wolframalpha.com/input/?i=solve%28%28%2840-3*x%29%2F2%29*%2820-2*x%29*x-500%2Cx%29
>
> > Is there anything I can do differently to make it find the real
solutions?
> > Thank you and kind regards
>
> > Joerg
>
>
>
> Example. Find real exact solutions of equation:
> (%i1) eq:((40-3*x)*(20-2*x)*x)/2-500=0 $
>
> I define function "solvet":
>
> (%i2) solvet(eq,x):=block([spr,k,maperror,mapprint],
> /* Copyright (C) 2013 Aleksas Domarkas */
> maperror:false, mapprint:false,
> spr:solve(eq,x), rectform(%%),
> if freeof(sin,%%) then return(sort(%%)) else
> makelist(x=map(polarform,rhs(spr[k])),k,1,length(spr)),
> rectform(%%),
> trigsimp(%%),
> sort(%%))$
>
> (%i3) solvet(eq,x);
> (%o3)
> [x=(20*sqrt(13)*cos(atan((3^(5/2)*sqrt(101))/103)/3)+70)/9,
> x=(20*sqrt(13)*cos((atan((3^(5/2)*sqrt(101))/103)-2*%pi)/3)+70)/9,
> x=(20*sqrt(13)*cos((atan((3^(5/2)*sqrt(101))/103)+2*%pi)/3)+70)/9]
> (%i4) float(%), numer;
> (%o4) [x=15.3584874666829,x=6.234149131052292,x=1.740696735598144]
> (%i5) sort(%);
> (%o5) [x=1.740696735598144,x=6.234149131052292,x=15.3584874666829]
>
> (%i6) allroots(eq); /* for test */
> (%o6) [x=1.740696735598142,x=6.234149131052291,x=15.3584874666829]
>
> Maple and Mathematica do not solve this problem( find real exact
solutions).
>
Nice. I tried with Solve, Reduce, Simplify, FullSimplify.
FullSimpify and Reduce both just restate that there are three
roots that solve the equation.
--John
>
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