# Questions tagged [algebraic-equations]

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### Algebraic solution for a system of algebraic equations?

How would one solve algebraically the following system of algebraic equations? $$f(a,b):=a(1-b)+ab\frac a{a+b}.$$ $$u = f(a,b),\quad v = f(b,a).$$ Solve algebraically $(a,b)$ in terms of $(u,v)$ ...
223 views

### Abel-Ruffini theorem for systems of polynomial equations

I know the Abel-Ruffini theorem, which states that a general polynomial equation in one variable with degree $\geq 5$ is not solvable in radicals. I wonder whether there is a similar result for ...
208 views

### Pair of two-variable cubic polynomial equations

Let us consider the following system of two polynomial equations of third order for two real numbers $x_1,x_2$: $$x_i (x_i + 2) (x_i + 4) - 2 a_i (x_1 + x_2 + 4) = 0,$$ $i =1,2$. Here $a_1 >0$ ...
353 views

### Closed-Form solution for system of simple nonlinear equations

I am interested in analytical solutions for a system of nonlinear equations. (The question was first asked at math.SE, where (after 1months and one rounds of bounty) there is only interesting ...
258 views

### Does this system have a closed-form solution? $x_j^2 = \sum_{i=1}^n B_{ij} x_i$

I am interested in solving the following system of $n$ equations: $$x_j^2 = \sum_{i=1}^n B_{ij} x_i$$ for all $j\in\{1,\dots,n\}$, where $n$ is a positive integer and all the $0\leq B_{ij}\leq 1$ ...
38 views

### Solving exponential system [closed]

How can i solve the following system? $\begin{cases} x^y = 16 \\ \frac{x}{y}=2\\ \end{cases}$ I tried everything, nothing works.
283 views

### Asymptotics of solution of transcendental equation [closed]

It seems the real solution of the following equation $$t=u^2+u\log(u)$$ has no closed form in view of the output of Reduce[t == u^2 + u*Log[u], u, Reals] The ...