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0
votes
2answers
53 views
Solution to a system of symmetric equations
After applying the Lagrange multiplier method, I got the following system of equations, which is quite symmetric:
$(x+y)^2 + (x+z)^2 = \frac{2}{3} \lambda x$
$(y+x)^2 + (y+z)^2 = \frac{2}{3} \lambda ...
1
vote
4answers
65 views
Solving a set of 3 Nonlinear Equations
In the following 3 equations:
$$
k_1\cos^2(\theta)+k_2\sin^2(\theta) = c_1
$$
$$
2(k_2-k_1)\cos(\theta)\sin(\theta)=c_2
$$
$$
k_1\sin^2(\theta)+k_2\cos^2(\theta) = c_3
$$
$c_1$, $c_2$ and $c_3$ are ...
4
votes
1answer
178 views
Do the momentum conservation equations have a unique solution?
In high energy physics, one often encounters conservation of momentum and energy equations of the following form:
$$\begin{array}{rcr}
\sum_i (-1)^{\alpha_i}\sqrt{k_i^2 + m_i^2} = 0 \\
\sum_i ...
2
votes
1answer
110 views
Checking if a System of Polynomial Equations is Consistent
I'm trying to determine whether any solutions exist to a system of $(n+1)$ polynomial equations in $n$ unknowns.
For example:
$$
\begin{align*}
xy&=-2\\
x^2-1&=0\\
y^3-3y^2+2y&=0
...
0
votes
0answers
168 views
4th degree nonlinear simultaneous equations with 3 unknowns
What method should be used to solve the following nonlinear simultaneous equations for $z_1, z_2, z_3$
$$a_2z_1^2 + a_1z_2^2 - (z_1z_2 \tan(t))^2 - z_1z_2 2b_1/\cos(t)^2 = b_1/\cos(t)^2 - a_1a_2$$
...
