MathDB

10.2

Part of 2005 Moldova National Olympiad

Problems(1)

System of equation

Source:

1/29/2010
Find all positive solution of system of equation: \frac{xy}{2005y\plus{}2004x}\plus{}\frac{yz}{2004z\plus{}2003y}\plus{}\frac{zx}{2003x\plus{}2005z}\equal{}\frac{x^{2}\plus{}y^{2}\plus{}z^{2}}{2005^{2}\plus{}2004^{2}\plus{}2003^{2}}