algsys and real solutions
- Subject: algsys and real solutions
- From: laurent couraud
- Date: Sat, 19 Aug 2006 02:44:14 +0200
solving this step by step by substitution method I found that:
[
[teta =
-((6*sqrt(3)-9)^(2/3)*(sqrt(3)*%i+1)+3*sqrt(3)*%i-6*(6*sqrt(3)-9)^(1/3)-3)/(4*(6*sqrt(3)-9)^(1/
3)),
teta =
((6*sqrt(3)-9)^(2/3)*(sqrt(3)*%i-1)+3*sqrt(3)*%i+6*(6*sqrt(3)-9)^(1/3)+3)/(4*(6*sqrt(3)-9)^(1/3
)),
teta = ((6*sqrt(3)-9)^(2/3)+3*(6*sqrt(3)-9)^(1/3)-3)/(2*(6*sqrt(3)-9)^(1/3))], => real!
[teta =
-((6*sqrt(3)-9)^(2/3)*(sqrt(3)*%i+1)+3*sqrt(3)*%i-6*(6*sqrt(3)-9)^(1/3)-3)/(4*(6*sqrt(3)-9)^(1/
3)),
teta =
((6*sqrt(3)-9)^(2/3)*(sqrt(3)*%i-1)+3*sqrt(3)*%i+6*(6*sqrt(3)-9)^(1/3)+3)/(4*(6*sqrt(3)-9)^(1/3
)),
teta = ((6*sqrt(3)-9)^(2/3)+3*(6*sqrt(3)-9)^(1/3)-3)/(2*(6*sqrt(3)-9)^(1/3)) => real!
]
]
[beta = -(sqrt(teta^4-16*teta^3+58*teta^2-48*teta+9)+teta^2-8*teta+9)/(2*teta^2-8*teta+6),
beta = (sqrt(teta^4-16*teta^3+58*teta^2-48*teta+9)-teta^2+8*teta-9)/(2*teta^2-8*teta+6)
]
[alpha = -(3*beta+3)/(2*beta*teta-3*beta-3)]
Laurent.
> -----Message d'origine-----
> De : maxima-admin at math.utexas.edu
> [mailto:maxima-admin at math.utexas.edu] De la part de Michel Gosse
> Envoy? : vendredi 18 ao?t 2006 10:35
> ? : maxima at math.utexas.edu
> Objet : [Maxima] algsys and real solutions
>
>
> Hello
>
> Solving the above system with algsys, i obtain only complex
> solutions. How can
> i obtain the real solutions of this system ?
>
> eq1: alpha * beta * teta / ( (alpha-1)*(beta+1) ) - 1.5
> eq2: alpha * beta * teta^2 / ( (alpha-2)*(beta+2) ) - 3
> eq3: alpha * beta * teta^3 / ( (alpha-3)*(beta+3) ) - 4.5
>
> algsys([eq1,eq2,eq3],[alpha,beta,teta]) returns no real solutions.
>
> Best regards
>
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