IMO Shortlist 1965 problem 2
Dodao/la: arhiva2. travnja 2012.
Consider the sytem of equations
. The coefficients satisfy the conditions:
are positive numbers;
b) the remaining coefficients are negative numbers;
c) in each equation, the sum ofthe coefficients is positive.
Prove that the given system has only the solution
Izvor: Međunarodna matematička olimpijada, shortlist 1965