Hello, you can help me please ?
Prove that is the only solution of the system :
clearly from the equations we have let so from the second equation we get: which with the first equation gives us:
obviously satisfies we'll show that that's the only real solution of to see this, let then:
thus and thereofore it is not possible for to have more than one real zero by Rolle's theorem. Q.E.D.
View the solution of your problems, for example, here (Problem 12, pages 29-30). You need a special program to view this file.
http://www.lix.polytechnique.fr/Labo...ardi/M00-06.ps
These two pages of evidence from the file.
Of course your solution is better, elegant. Just by chance I found it on the Internet and suggested as a possible solution.
Incidentally, this problem was proposed by professor of my university for entrance examinations on Department of Mechanics and Mathematics. As far as I know this problem to fully solve only two entrants.