# Tagged Questions

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### Solving a quadratic system of equations for a single variable

I have a quadratic system of $n$ equations that looks like: $$(A_{j}^{i}y + B_{j}^{i})x_{j}=0$$ For $i=0...n$. $A_{i,j}$ and $B_{ij}$ are integer matrices and sums over $j$ are implied. $j$ runs ...
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### Polynomial systems - conditions for real solution

I was working on the computation of equilibrium points for dynamical systems and arrived in the following system of $n$ polynomials in the variables $(x_1,\ldots,x_n)$ \begin{equation*} ...
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### Solve $x+3y=4y^3,y+3z=4z^3 ,z+3x=4x^3$ in reals

Find answers of this system of equations in reals$$\left\{ \begin{array}{c} x+3y=4y^3 \\ y+3z=4z^3 \\ z+3x=4x^3 \end{array} \right.$$ Things O have done: summing these 3 equations give ...
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### Solving for a single variable in a quadratic system

I have a quadratic system of $n$ equations that looks like: $$A_{ij}x_{j}y + B_{ij}x_{j}=0$$ For $i=0...n$, where $A_{i,j}$ and $B_{ij}$ are integer matrices and sums over $j$ are implied. Is there ...
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### Solving a cubic equation system

I got a cubic equation system that contains 3 cubic equations with 3 variables. I want to find the number of solutions and the solutions themselves (as a numerical approximation). Do you know good ...
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### Bound for the number of solutions of a polynomial system of equation.

Given integers $d_1,\ldots,d_n$, is there an elementary way to justify that for generic polynomials $f_1,\ldots,f_n\in\mathbb{C}[X_1,\ldots,X_n]$ of degree less or equal than $d_1,\ldots,d_n$, the ...
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### How can I show that there are only finitely many solutions for the following system?

$x^2+yz=x$ $y^2+zx=y$ $z^2+xy=z$ I could not do anything to find the solutions. Please give some hints.
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### Given ${x^2-x y+y^2 = 15, x y+x+y = 13}$ find the value of $x^2+6y$

Both x and y are real numbers and x > y . Given ${x^2-x y+y^2 = 15, x y+x+y = 13}$ find the value of $x^2+6y$ . I tried solving the second equation to get $y=(13-x)/(x+1)$ and substituted that in ...
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### How to solve this system for real $x,y,z$

Find the real values $x,y,z$ such that $$\begin{cases} x+y^2+z^3=21\qquad (1)\\ y+z^2+x^3=71\qquad (2)\\ z+x^2+y^3=45\qquad (3) \end{cases}$$ Thank you everyone. This problem have some nice methods, ...
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### Solve a set of non linear Equations on Galois Field

I have the following set of equations: $$M_{1}=\frac{y_1-y_0}{x_1-x_0}$$ $$M_{2}=\frac{y_2-y_0}{x_2-x_0}$$ $M_1, M_2, x_1, y_1, x_2, y_2,$ are known and they are chosen from a $GF(2^m).$ I want to ...
### system of equations solving for positive $a,b,c$
i need help i need to find positive number $a,b,c$ solving this system of equations? $$(1-a)(1-b)(1-c)=abc$$ $$a+b+c=1$$ I found that $0<a,b,c<1$ and I try to solve it by try $(1-a)=a$, ...
If α ,β ,γ are three numbers s.t.: $\ α^ \$ + $\ β \$ + $γ \$ = −2 $\ α^2 \$ + $\ β^2 \$ + $γ^2 \$ = 6 $\ α^3 \$ + $\ β^3 \$ + $γ^3 \$ = −5, then $\ α^4 \$ + $\ β^4 \$ + ... 1answer 82 views ### Help with non-linear system of equations This system of equations \begin{align} xy+yz+zx & =3 \\ \\ x^4+y^4+z^4 & =3\end{align} How to solve this system of equations? Any help, Plz. Thank all 1answer 145 views ### Visualise 3 simultaneous cubic equations I have three equations of the form: $$\frac{i_1^3}{P_1}+i_1(Z_1+Z_2)+(i_2+i_3)Z_2-U_1=0$$ $$\frac{i_2^3}{P_2}+i_2(Z_1+Z_2)+(i_1+i_3)Z_2-U_2=0$$ $$\frac{i_3^3}{P_3}+i_3(Z_1+Z_2)+(i_1+i_2)Z_2-U_3=0$$ ... 1answer 68 views ### number of solutions in homogeneous system What is the maximum possible number of solutions of homogeneous systemN \times N$($N$variables,$N$equations) of degree$2$, where in each equation we have linear terms in$x_i$and quadratic ... 2answers 430 views ### The system of equations$x^2 + y^2 - x - 2y = 0$and$x + 2y = c$I have$(1.) \quad x^2 + y^2 - x - 2y = 0 \\ (2.) \quad x + 2y = c$Solving for$y$in$(2.)$gives$y = (c - x) / 2$Is there a way to simplify equation$(1.)$? Because at the end I arrive at ... 2answers 305 views ### Solving 3 simultaneous cubic equations I have three equations of the form: $$i_1^3L_1+i_1K+V_1+(i_2+i_3+C)Z_n=0$$ $$i_2^3L_2+i_2K+V_2+(i_1+i_3+C)Z_n=0$$ $$i_3^3L_3+i_3K+V_3+(i_1+i_2+C)Z_n=0$$ where$L_1,L_2,L_3,K,V_1,V_2,V_3,C$and$Z_n$... 3answers 113 views ### Simultaneous solution(s) to$a^2+4b^2+4ab=0$and$a^2+4b^2+32+16a-8b=0\$?
Could you tell me just how should I solve this system: $$a^2+4b^2+4ab=0\\ a^2+4b^2+32+16a-8b=0$$ I can't remember the proceeding and it's driving me crazy. Thanks a lot