解x²-4xy+5y²-2y+1=0(x²-4xy+4y²)+(y²-2y+1)=0(x-2y)²+(y-1)²=0∵(x-2y)²≥0 (y-1)²≥0∴x-2y=0 y-1=0∴y=1，x=2∴x²-y^2009=4-1=3
(x-2y)^2+(y-1)^2=0所以x=2y，y=1所以x=2(x^2-y)^2009=3^2009
