Hello, you can help me please ?

Prove that is the only solution of the system :

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- April 1st 2009, 03:18 PMlinda2005System
Hello, you can help me please ?

Prove that is the only solution of the system : - April 2nd 2009, 06:40 AMNonCommAlg
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. - April 2nd 2009, 08:21 AMDeMath
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.

http://s47.radikal.ru/i115/0904/99/559e3cce7fbat.jpg - April 2nd 2009, 04:46 PMNonCommAlg
- April 2nd 2009, 06:04 PMDeMath
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 (Happy)(Doh) on Department of Mechanics and Mathematics. As far as I know this problem to fully solve only two entrants.