7
votes
1answer
356 views

The solutions for the equation $\frac{a}{c-b+1}+\frac{b}{a-c+1}+\frac{c}{b-a+1}=0.$

How can I find the solution for the following equation in $a,b \mbox{ and } c$. $$\frac{a}{c-b+1}+\frac{b}{a-c+1}+\frac{c}{b-a+1}=0.$$ Also $b-c \neq 1$, $c-a \neq 1$ and $a-b \neq 1$. Thanks!
3
votes
2answers
64 views

Solving $L= \frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ac}+\frac{c^2}{2c^2+ab}$ priveded $a+b+c=0$

Let $a,b,c$ be such that $a+b+c=0$ and suppose that $$L= \frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ac}+\frac{c^2}{2c^2+ab}.$$ Find the value of $L$. I can only see the symmetry of these function ...
1
vote
0answers
79 views

Geometry aspect of a extreme value problem

In a plain with orthogonal coordinate $XOY$, set point $A(a,a)$, and $P$ is a point in function $y=\frac{1}{x}$,where $x>0$. If the distance between $P$ and $A$ is $2\sqrt{2}$.Find all $a$ ...
1
vote
0answers
52 views

When the system of equations below had a solution?

The system of equations is $$\begin{cases} \frac{c_1}{1-x_1}+\frac{c_2}{1-x_2}+\frac{c_3}{1-x_3}=0\\ \frac{c_1}{k-x_1}+\frac{c_2}{k-x_2}+\frac{c_3}{k-x_3}=0\\ ...
1
vote
1answer
119 views

I wonder whether the system of equations and inequations below have a solution.

I wonder whether the system of equations and inequations below have a solution. If there are solutions, what are they? A numerical solution is also desired. $$\begin{cases} ...
1
vote
1answer
66 views

Help explain method to solve two equations in two unknowns where one of the variables has a square term

Given: $-\frac{96}{x^2y}+1+y=0$ $-\frac{96}{xy^2}+2+x=0$ Solve for $x$ and $y$ How should I find $x$ and $y$? I thought of using the methods I learned in linear algebra but then I noticed that ...
2
votes
2answers
40 views

Technique to solve this equation of 2 unkowns

I was solving a problem of single phase eletrical circuits where I had to find the inductor $L$ and resistance $R$. I managed to get two equations containing the two unknowns. ...
0
votes
1answer
48 views

Does analytic closed-form solution exist

I have a polynomial (degree 6) that is form by multiplication of two smaller polynomials (degree 4 and 2) $H(x) = 1+ax+bx^2+cx^3+dx^4)(u+vx+x^2) = \\u+ (a u+v)x + (a v+b u+1) x^2 + (a+b v+c u)x^3 ...