非零实数x、y满足（x2+2009-x）（y2+2009-y）=2009，则x+2008y2008x+y=．

Question

非零实数x、y满足（√(x2+2009)-x）（√(y2+2009)-y）=2009，则(x+2008y)/(2008x+y)=______．

Answer 1

当x+y=0，即x=-y时，（√(x2+2009)-x）（√(y2+2009)-y）=2009恒成立，
则(x+2008y)/(2008x+y)=(−y+2008y)/(−2008y+y)=(2007y)/(−2007y)=-1．
故答案为：-1