Register to reply

System of cross-polynomials of variable degree

by ydydry
Tags: crosspolynomials, degree, variable
Share this thread:
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
Researcher figures out how sharks manage to act like math geniuses
Math journal puts Rauzy fractcal image on the cover
Heat distributions help researchers to understand curved space

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