Quadratic simultaneous equations with three variables
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I am looking for an analytical solution of the following quadratic simultaneous equations.
$$(1) x^2-a_0(b_0-x-z)(c_0-y-x)=0$$
$$(2) y^2-a_1(b_1-y-x)(c_1-z-y)=0$$
$$(3) z^2-a_2(b_2-z-y)(c_2-x-z)=0$$
where $x$, $y$, and $z$ are variables; $a_i$, $b_i$, and $c_i$ ($i=0,1,2$) are constants.
I tried with Maple, but i couldn't get the solution...
systems-of-equations nonlinear-system
asked Nov 22 at 9:12
Sun Yong Kwon
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up vote
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I am looking for an analytical solution of the following quadratic simultaneous equations.
$$(1) x^2-a_0(b_0-x-z)(c_0-y-x)=0$$
$$(2) y^2-a_1(b_1-y-x)(c_1-z-y)=0$$
$$(3) z^2-a_2(b_2-z-y)(c_2-x-z)=0$$
where $x$, $y$, and $z$ are variables; $a_i$, $b_i$, and $c_i$ ($i=0,1,2$) are constants.
I tried with Maple, but i couldn't get the solution...
systems-of-equations nonlinear-system
asked Nov 22 at 9:12
Sun Yong Kwon
1
New contributor
Sun Yong Kwon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to math.SE, can you explain more? like where you faced problem in using Maple?
– tarit goswami
Nov 22 at 9:16
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am looking for an analytical solution of the following quadratic simultaneous equations.
$$(1) x^2-a_0(b_0-x-z)(c_0-y-x)=0$$
$$(2) y^2-a_1(b_1-y-x)(c_1-z-y)=0$$
$$(3) z^2-a_2(b_2-z-y)(c_2-x-z)=0$$
where $x$, $y$, and $z$ are variables; $a_i$, $b_i$, and $c_i$ ($i=0,1,2$) are constants.
I tried with Maple, but i couldn't get the solution...
systems-of-equations nonlinear-system
asked Nov 22 at 9:12
Sun Yong Kwon
1
New contributor
Sun Yong Kwon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I am looking for an analytical solution of the following quadratic simultaneous equations.
$$(1) x^2-a_0(b_0-x-z)(c_0-y-x)=0$$
$$(2) y^2-a_1(b_1-y-x)(c_1-z-y)=0$$
$$(3) z^2-a_2(b_2-z-y)(c_2-x-z)=0$$
where $x$, $y$, and $z$ are variables; $a_i$, $b_i$, and $c_i$ ($i=0,1,2$) are constants.
I tried with Maple, but i couldn't get the solution...
systems-of-equations nonlinear-system
systems-of-equations nonlinear-system
asked Nov 22 at 9:12
Sun Yong Kwon
1
New contributor
Sun Yong Kwon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 22 at 9:12
Sun Yong Kwon
1
New contributor
Sun Yong Kwon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 22 at 9:12
Sun Yong Kwon
1
New contributor
Sun Yong Kwon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 22 at 9:12
Sun Yong Kwon
1
asked Nov 22 at 9:12
Sun Yong Kwon
1
1
New contributor
Sun Yong Kwon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Sun Yong Kwon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Sun Yong Kwon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to math.SE, can you explain more? like where you faced problem in using Maple?
– tarit goswami
Nov 22 at 9:16
add a comment |
Welcome to math.SE, can you explain more? like where you faced problem in using Maple?
– tarit goswami
Nov 22 at 9:16
Welcome to math.SE, can you explain more? like where you faced problem in using Maple?
– tarit goswami
Nov 22 at 9:16
Welcome to math.SE, can you explain more? like where you faced problem in using Maple?
– tarit goswami
Nov 22 at 9:16
add a comment |
1 Answer
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0
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I think that you are facing a monster !
You could reduce the problem to two equations $x,y$ eliminating $z$ from equation $(1)$. Replacing in $(2)$ and $(3)$ is just awful. You should end with a polynomial of degree $6$ in $x$ or $y$. Then, this explains that.
For illustration purposes, I used $a_i=i+1$, $b_i=a_i+1$, $c_i=b_i+1$ $(i=0,1,2)$. There are six real solutions ${x_k,y_k,z_k}$ $(k=1,2,cdots,6)$, which express as functions of the roots of polynomial
$$t^6-324 t^4+3312 t^3-12276 t^2+19008 t-10368=0$$
answered Nov 22 at 10:07
Claude Leibovici
116k1156131
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
I think that you are facing a monster !
You could reduce the problem to two equations $x,y$ eliminating $z$ from equation $(1)$. Replacing in $(2)$ and $(3)$ is just awful. You should end with a polynomial of degree $6$ in $x$ or $y$. Then, this explains that.
For illustration purposes, I used $a_i=i+1$, $b_i=a_i+1$, $c_i=b_i+1$ $(i=0,1,2)$. There are six real solutions ${x_k,y_k,z_k}$ $(k=1,2,cdots,6)$, which express as functions of the roots of polynomial
$$t^6-324 t^4+3312 t^3-12276 t^2+19008 t-10368=0$$
answered Nov 22 at 10:07
Claude Leibovici
116k1156131
add a comment |
up vote
0
down vote
I think that you are facing a monster !
You could reduce the problem to two equations $x,y$ eliminating $z$ from equation $(1)$. Replacing in $(2)$ and $(3)$ is just awful. You should end with a polynomial of degree $6$ in $x$ or $y$. Then, this explains that.
For illustration purposes, I used $a_i=i+1$, $b_i=a_i+1$, $c_i=b_i+1$ $(i=0,1,2)$. There are six real solutions ${x_k,y_k,z_k}$ $(k=1,2,cdots,6)$, which express as functions of the roots of polynomial
$$t^6-324 t^4+3312 t^3-12276 t^2+19008 t-10368=0$$
answered Nov 22 at 10:07
Claude Leibovici
116k1156131
add a comment |
up vote
0
down vote
up vote
0
down vote
I think that you are facing a monster !
You could reduce the problem to two equations $x,y$ eliminating $z$ from equation $(1)$. Replacing in $(2)$ and $(3)$ is just awful. You should end with a polynomial of degree $6$ in $x$ or $y$. Then, this explains that.
For illustration purposes, I used $a_i=i+1$, $b_i=a_i+1$, $c_i=b_i+1$ $(i=0,1,2)$. There are six real solutions ${x_k,y_k,z_k}$ $(k=1,2,cdots,6)$, which express as functions of the roots of polynomial
$$t^6-324 t^4+3312 t^3-12276 t^2+19008 t-10368=0$$
answered Nov 22 at 10:07
Claude Leibovici
116k1156131
I think that you are facing a monster !
You could reduce the problem to two equations $x,y$ eliminating $z$ from equation $(1)$. Replacing in $(2)$ and $(3)$ is just awful. You should end with a polynomial of degree $6$ in $x$ or $y$. Then, this explains that.
For illustration purposes, I used $a_i=i+1$, $b_i=a_i+1$, $c_i=b_i+1$ $(i=0,1,2)$. There are six real solutions ${x_k,y_k,z_k}$ $(k=1,2,cdots,6)$, which express as functions of the roots of polynomial
$$t^6-324 t^4+3312 t^3-12276 t^2+19008 t-10368=0$$
answered Nov 22 at 10:07
Claude Leibovici
116k1156131
answered Nov 22 at 10:07
Claude Leibovici
116k1156131
answered Nov 22 at 10:07
Claude Leibovici
116k1156131
answered Nov 22 at 10:07
Claude Leibovici
116k1156131
116k1156131
add a comment |
add a comment |
Sun Yong Kwon is a new contributor. Be nice, and check out our Code of Conduct.
Sun Yong Kwon is a new contributor. Be nice, and check out our Code of Conduct.
Sun Yong Kwon is a new contributor. Be nice, and check out our Code of Conduct.
Sun Yong Kwon is a new contributor. Be nice, and check out our Code of Conduct.
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Welcome to math.SE, can you explain more? like where you faced problem in using Maple?
– tarit goswami
Nov 22 at 9:16