System of cross-polynomials of variable degree

by ydydry
Tags: crosspolynomials, degree, variable
ydydry is offline
Mar4-13, 09:17 AM
P: 1
Dear all,

I am stuck with an apparently easy system of 3 simultaneous equations that has to be solved in x,y and z. The system is the following:


The parameters (a,b,c) and the variables (x,y,z) are all in ℝ₊. The parameter α is in the open interval (0,1), so that the problem is not trivial. The question is for which α there exists a closed-form solution, and for which α there exists none, given a general vector (a,b,c).

Proving that there always exist a unique solution is trivial as in each equation the right-hand sides are always increasing, whereas the left-hand sides are always decreasing in the corresponding variable (x for the first, y for the second, z for the third).

Hence, my problem is in the existence of a closed-form solution.

Many thanks!!
Phys.Org News Partner Mathematics news on
Math modeling handbook now available
Hyperbolic homogeneous polynomials, oh my!
Researchers help Boston Marathon organizers plan for 2014 race

Register to reply

Related Discussions
Solving polynomials for variable (x) Calculus & Beyond Homework 2
Subspaces of polynomials with degree <= 2 Calculus & Beyond Homework 4
set of degree 2 polynomials a subspace Calculus & Beyond Homework 2
Subspace of Polynomials of degree 2 Linear & Abstract Algebra 11
Irreducible Polynomials p 5 degree 4 Linear & Abstract Algebra 1