Hello, you can help me please ?
Prove that is the only solution of the system :
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.
These two pages of evidence from the file.
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.