Can anyone help to solve these equations of system?

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The equations of system is given for three variables $rho$, $e$ and $l$ as



$$
rho ^3 left(e^2-2 l epsilon -1right)-l^2 rho +2 l^2+rho ^2 (4 l epsilon +2)-epsilon^2 rho^5+2 rho ^4 epsilon ^2= 0 ,
$$
$$
l^2 rho -3 l^2+rho ^2 (-2 l epsilon -1)-epsilon^2 rho^5+rho ^4 epsilon ^2 = 0 ,
$$
$$
-3 l^2 rho +12 l^2+rho ^2 (4 l epsilon +2)-epsilon^2 rho^5=0 ,
$$
where $epsilon$ is free parameter. Is it possible to get an analytical solutions of these equation?




calculus real-analysis analysis




share|cite|improve this question






















  • Do you want to solve for $$rho,e$$ and $$l$$?
    – Dr. Sonnhard Graubner
    Aug 13 at 11:15










  • Am I right in assuming the last expression equals zero too?
    – Bruce
    Aug 13 at 11:16










  • yes I have missed to put "=0"
    – Bturimov
    Aug 13 at 11:37










  • You could start by combining the last two equations to eliminate $l^2$. It would still involve $l$ but may be a start.
    – Bruce
    Aug 13 at 11:39











  • You should give some context for the system of equations.
    – Somos
    Aug 13 at 14:15














up vote
-3
down vote

favorite












The equations of system is given for three variables $rho$, $e$ and $l$ as



$$
rho ^3 left(e^2-2 l epsilon -1right)-l^2 rho +2 l^2+rho ^2 (4 l epsilon +2)-epsilon^2 rho^5+2 rho ^4 epsilon ^2= 0 ,
$$
$$
l^2 rho -3 l^2+rho ^2 (-2 l epsilon -1)-epsilon^2 rho^5+rho ^4 epsilon ^2 = 0 ,
$$
$$
-3 l^2 rho +12 l^2+rho ^2 (4 l epsilon +2)-epsilon^2 rho^5=0 ,
$$
where $epsilon$ is free parameter. Is it possible to get an analytical solutions of these equation?




calculus real-analysis analysis




share|cite|improve this question






















  • Do you want to solve for $$rho,e$$ and $$l$$?
    – Dr. Sonnhard Graubner
    Aug 13 at 11:15










  • Am I right in assuming the last expression equals zero too?
    – Bruce
    Aug 13 at 11:16










  • yes I have missed to put "=0"
    – Bturimov
    Aug 13 at 11:37










  • You could start by combining the last two equations to eliminate $l^2$. It would still involve $l$ but may be a start.
    – Bruce
    Aug 13 at 11:39











  • You should give some context for the system of equations.
    – Somos
    Aug 13 at 14:15












up vote
-3
down vote

favorite









up vote
-3
down vote

favorite











The equations of system is given for three variables $rho$, $e$ and $l$ as



$$
rho ^3 left(e^2-2 l epsilon -1right)-l^2 rho +2 l^2+rho ^2 (4 l epsilon +2)-epsilon^2 rho^5+2 rho ^4 epsilon ^2= 0 ,
$$
$$
l^2 rho -3 l^2+rho ^2 (-2 l epsilon -1)-epsilon^2 rho^5+rho ^4 epsilon ^2 = 0 ,
$$
$$
-3 l^2 rho +12 l^2+rho ^2 (4 l epsilon +2)-epsilon^2 rho^5=0 ,
$$
where $epsilon$ is free parameter. Is it possible to get an analytical solutions of these equation?




calculus real-analysis analysis




share|cite|improve this question














The equations of system is given for three variables $rho$, $e$ and $l$ as



$$
rho ^3 left(e^2-2 l epsilon -1right)-l^2 rho +2 l^2+rho ^2 (4 l epsilon +2)-epsilon^2 rho^5+2 rho ^4 epsilon ^2= 0 ,
$$
$$
l^2 rho -3 l^2+rho ^2 (-2 l epsilon -1)-epsilon^2 rho^5+rho ^4 epsilon ^2 = 0 ,
$$
$$
-3 l^2 rho +12 l^2+rho ^2 (4 l epsilon +2)-epsilon^2 rho^5=0 ,
$$
where $epsilon$ is free parameter. Is it possible to get an analytical solutions of these equation?





calculus real-analysis analysis





share|cite|improve this question













share|cite|improve this question




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edited Aug 13 at 11:37

























asked Aug 13 at 11:05









Bturimov

52




52











  • Do you want to solve for $$rho,e$$ and $$l$$?
    – Dr. Sonnhard Graubner
    Aug 13 at 11:15










  • Am I right in assuming the last expression equals zero too?
    – Bruce
    Aug 13 at 11:16










  • yes I have missed to put "=0"
    – Bturimov
    Aug 13 at 11:37










  • You could start by combining the last two equations to eliminate $l^2$. It would still involve $l$ but may be a start.
    – Bruce
    Aug 13 at 11:39











  • You should give some context for the system of equations.
    – Somos
    Aug 13 at 14:15
















  • Do you want to solve for $$rho,e$$ and $$l$$?
    – Dr. Sonnhard Graubner
    Aug 13 at 11:15










  • Am I right in assuming the last expression equals zero too?
    – Bruce
    Aug 13 at 11:16










  • yes I have missed to put "=0"
    – Bturimov
    Aug 13 at 11:37










  • You could start by combining the last two equations to eliminate $l^2$. It would still involve $l$ but may be a start.
    – Bruce
    Aug 13 at 11:39











  • You should give some context for the system of equations.
    – Somos
    Aug 13 at 14:15















Do you want to solve for $$rho,e$$ and $$l$$?
– Dr. Sonnhard Graubner
Aug 13 at 11:15




Do you want to solve for $$rho,e$$ and $$l$$?
– Dr. Sonnhard Graubner
Aug 13 at 11:15












Am I right in assuming the last expression equals zero too?
– Bruce
Aug 13 at 11:16




Am I right in assuming the last expression equals zero too?
– Bruce
Aug 13 at 11:16












yes I have missed to put "=0"
– Bturimov
Aug 13 at 11:37




yes I have missed to put "=0"
– Bturimov
Aug 13 at 11:37












You could start by combining the last two equations to eliminate $l^2$. It would still involve $l$ but may be a start.
– Bruce
Aug 13 at 11:39





You could start by combining the last two equations to eliminate $l^2$. It would still involve $l$ but may be a start.
– Bruce
Aug 13 at 11:39













You should give some context for the system of equations.
– Somos
Aug 13 at 14:15




You should give some context for the system of equations.
– Somos
Aug 13 at 14:15















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