The algebraic-equations tag has no wiki summary.

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### Is there any method to solve a Bivariate Cubic Equation System? [closed]

$f(x, y) = 0$ and $g(x, y) = 0$,
both $f$ and $g$ are cubic polynomial equation (at most 10 coefficients for each).
Is there any fixed method to solve this degenerate equation system?
thanks.

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148 views

### how to solve system of congruence with multivariables [closed]

There n variables x1,x2,...,xn represented as X, n equations whose coefficient matrix (n*n) is represented as A, and this system ...

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373 views

### how to solve this multivariate quadratic equation?

This has been posted on math.stackexchange but got just one partial(insightful though) comment. I'm posting it here in a hope of getting further ideas and comments:
The problem was:
Any hope to ...

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**2**answers

766 views

### Real root of a cubic equation [closed]

I have a function f(x,n) can be expressed as a cubic function of x with coefficients that are functions of n. For example x^3 + (n-2)x^2 + (3n-6)x + n.
I want to prove that for every positive value ...

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### Random variables related through nonlinear system of equations

I asked this question on http://math.stackexchange.com/questions/377140/random-variables-related-through-nonlinear-system-of-equations, however I received no answer for a while so I'm posting it here:
...

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### System of two variables quadratic equations

Let $\mathcal{P}_{2,Z}$ be the set of all 2 variables quadratic equations $P(x,y)$ with integral coefficients: $$P(x,y)=a_1x^2+a_2y^2+a_3xy+a_4x+a_5y+a_6\ \ \ \ \ \ (a_i\in \mathbb{Z})$$
Consider a ...

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343 views

### equation for bowling ball on a trampoline

i´m searching for the displacement of the surface of a elastic rectangle for a given x and y and a force at a position.
like a bowling ball on a trampoline
the equation should include a var for the ...

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**1**answer

221 views

### Equations of the Hirzebruch surface embedded in a large space.

Let $\mathbb{F}_1$ be the Hirzebruch surface $\mathbb{P}(\mathcal{O}\oplus\mathcal{O}(-1))$ and let $D$ be the very ample divisor $3C_0+5f$ on $\mathbb{F}_1$ (notation as in [Hartshorne, Algebraic ...

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**1**answer

341 views

### Is there an analytical method of solving general square root equations?

Equations such as $\sqrt{x+1}+\sqrt{x+2}=x+3$ are easily solvable by squaring both sides. But if we increase an extra square root, like if trying to solve $\sqrt{x+1}+\sqrt{x+2}+\sqrt{x+3}=x+4$ we ...

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### Is this a known/solvable problem? (System of algebraic equations)

Hi there,
I am trying to find complex solutions with positive real part $\{t_j \;|\;{\rm Re}\;t_j>0,
j = 1, 2, 3, \dots, n\}$ of the system of equations
$$0 = 1 + \sum_j \left(t_j^{2l+1} + ...

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218 views

### solving in x involving both exponential and logarithmic function

Is it possible to solve a function with both exponential and logarithm such as
$a x^2 - b.\log(x) = c $
in closed form; where $a,b,c$ are constants and $a>0$ and $b>0$?

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**2**answers

516 views

### When is the degree of this number 3?

I am helping a friend of mine, that works in history of mathematics. She is studying the story of the solution of the cubic equation by Cardano. Sometimes she asks me some mathematical questions, that ...

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### An equation about generating functions and subfactorial

As I promised, I clone the problem from Math.SE to here, in order to find a solution.
Suppose $G_n(w)$ is a formal power series (really a probability generating function, see the following ...

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**1**answer

121 views

### expanding the sqare of sum

If there any way to expand the following?
$$\left(\sum_{i=1}^nx_i\right)^{\frac{1}{2}}$$
and more generally, a way to expand
$$\left(\sum_{i=1}^nx_i\right)^{\frac{p}{q}}$$
where $gcd(p,q) = 1$
...

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**1**answer

534 views

### Can roots of any polynomial be expressed using Eulerian function?

I encountered an interesting function which is called "Eulerian" by the Wolfram's MathWorld:
$$\phi(q)=\prod_{k=1}^{\infty} (1-q^{k})$$
It is interesting because it is claimed that roots of any ...

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489 views

### For any $n$, does there exist a number field with at least $n$ solutions to the unit equation

Let $n$ be a positive integer.
Does there exist a number field $K$ such that the number of solutions of the unit equation $$a+b =1, \quad a,b\in O_{K}^\ast$$ is at least $n$? Can we write down such a ...

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**0**answers

118 views

### satisfiable polynomial equations for given free coefficients

Let $F$ be a finite field, $n, k, m$ be natural numbers.
I give you $m$ vectors $c^{(1)},\ldots,c^{(m)}\in F^n$.
I ask for polynomials $p_1,\ldots,p_n$ on $k$ variables over $F$ such that the system ...

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356 views

### Bivariate polynomials with special properties

I recently came across some polynomials with some remarkable properties.
A polynomial $P(u,v) \in \mathbb{R}[u,v]$ in 2 variables is remarkable if
the set of solutions to the system ...

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### Can Fuchsian functions solve the general equation of degree n?

In the classic textbook Introduction to the Theory of Equations (Conkwright, 1941), on p. 85, the author writes that “the algebraic solution of the general equation of degree n is impossible if n is ...