# Tagged Questions

This tag indicates that several equations (of some type) must all hold. Do not use alone! Use in conjunction with (linear-algebra), (polynomials), (pde), (differential-equations), (inequalities) or another tag that describes the nature of the equations being considered.

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### A question about a system of PDE

It is well known that under suitable conditions, the symmetry of mixed second partial derivatives reads: $$\frac{\partial^2 f}{\partial x \partial y}=\frac{\partial^2 f}{\partial y \partial x}.$$ ...
68 views

### A general method for solving systems of quadratic equations

For linear systems we have general methods (i.e. Gauss elimination). Is there a general method for solving systems of quadratic equations with many variables? I heard about Groebner bases; is there ...
29 views

### consistency of solution question

Let $A, B$ be $n\times n$ matrices and $c, d$ be $n \times 1$ vectors such that the matrix equations $$Ax = c$$ $$Bx = d$$ are consistent, i.e., each equation admits a solution. Can we conclude that ...
73 views

### $x+y = 1$ and $\frac{1}{x} + \frac{1}{y} = 1$ Solve $x^3 + y^3$ [closed]

$x$, $y$ are complex numbers, $x$ and $y$ aren't $0$. $$x + y = 1$$ $$\frac{1}{x} + \frac{1}{y} = 1$$ $$x^3 + y^3 = ?$$ Thank You!
84 views

### Another troubling system of equations

I've been working on solving some linear equations arising from different optimization problems, but I keep getting stuck. Right now I have the problem below: I am trying to solve the system of ...
78 views

### Using equation to find value of $1/x - 1/y$

$$\left(\frac{48}{10}\right)^x=\left(\frac{8}{10}\right)^y=1000$$ What is the value of $\frac{1}{x}-\frac{1}{y}$? I have already used that when $48$ divided by $10$ then it becomes $4.8$ and when $8$ ...
22 views

### What is the best time complexity for this case?

I only want to know if the following system has any integer solution or not. Actually, I do not need to know the solution(s), and only need to know the answer of question "Does the system have any ...
18 views

### Set of 3 inequations involving 3 unknowns with a maximum

I am capable of finding a relation between unknowns x, y and z involved in this set of 3 inequations: $\begin{cases} ax - y - z \leq x \\ -x + by - z \leq y \\ - x - y + cz \leq z\end{cases}$ This ...
31 views

### Given a set of arbitrary data, is it possible to model this data using differential functions.

Problem At the moment, I have a problem with seven variables: $S, A_1, A_2, R_1, R_2, P_0, P_1$ and $P_2$. Each of these variables draws a smooth line through time. My question is, is there any ...
135 views

182 views

### Equivalence of system of nonlinear equations

Let $A\in\mathbb{R}^{n\times n}$ be a positive semidefinite matrix, $b\in\mathbb{R}^n$, $k>0$, and $g:\mathbb{R}^n\rightarrow\mathbb{R}$ be a positive function. Consider the system of nonlinear ...
26 views

### Can I solve these simultaneous questions, and if so, how?

I have a set of paired experimental observations (Fo, Bo), e.g. 1.55, 8.52 4.56, 36.36 21.03, 64.98 (> 6 data pairs in total) which I believe can be modelled as being generated by Fo = Ft + a.Bt ...
61 views

### System of equations in a,b,c,d

$a,b,c,d$ are complex numbers satisfying \begin{cases} a+b+c+d=3 \\ a^2+ b^2+ c^2+ d^2=5 \\ a^3+ b^3+ c^3+ d^3=3 \\ a^4+ b^4+ c^4+ d^4=9 \end{cases} Find the value of the following: ...
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### Another trigonometric moment problem

Is there a standard approach for solving the following system: $$m_k = \sum_{j=1}^N a_j e^{-2\pi i \mu_j k \delta}, \quad k = 0, 1, 2, \ldots,$$ where $N \in \mathbb{N}$, $m_k \in \mathbb{C}$, ...
640 views

### Why are the coefficients always equal?

Take the equation $ax^{2} + bx + c = 3x^{2} + 4x + 53$. Why is it always true that $a = 3, b = 4$ and $c = 53$? I've seen many examples like this where the coefficients are equated, and was just ...
68 views

### Underdetermined vs Overdetermined Problem

I'm trying to create a model which is of the form $$y = (a_0 + a_1l)[b_0+\sum_{m=1}^M b_m\cos(mx-\alpha_m)] [c_0 +\sum_{n=1}^N c_n\cos(nz-\beta_n)]$$ In the above system, $l$,$x$ and $z$ are ...
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### Grasping “Substitution” in terms of linear algebra

So I have a set of equations: $$x_{1} + x_{2} = 1$$ $$x_{2} + x_{4} = 3$$ From linear algebra, we know that (say, we're in $\mathbb{R}^{4}$, i.e. we have 4 variables), the solution space to the ...
25 views

### How can I solve this specific set of equations?

Here are the equations: $$\sum_{k = 1}^n i_k + Y_n u_n = J \quad \quad (1)$$ $$i_1 + Y(u_1 - u_2) = J \quad \quad (2)$$ i_k - Y(u_{k - 1} -2u_{k} + u_{k + 1}) = 0, \quad \quad k = 2, ..., n - 2 ...
66 views

### How to solve this system of equations for $x^2+y^2+z^2$?

For the complex numbers $x,y,z$, the system of equations $x^2-yz=i~~~~~ y^2-zx=i~~~~~ z^2-xy=i$ It is not easy for me to get $x^2+y^2+z^2$ from the above. I don't need the values of $x,y,z$ I'm ...
Sometimes if I randomly combine different equation and try to solve for a variable, one of them will cancel out. Why? For example: $\displaystyle x^2 = 4y^2$ and $\displaystyle x = 2y + 1$ And solve ...
Im currently doing my Kumon (A math tutoring center I guess) homework, and Im having a bit of difficulty answering a simultaneous equation, involving $x$ and $y$ variables to the second power. School ...