5a^2+2001a+9=0----(1)
9b^2+2001b+5=0----(2)
(1)两边乘以b^2,得：5a^2b^2+2001ab^2+9b^2=0----(3)
用(3)-(2),得：5(a^2b^2-1)+2001b(ab-1)=0,由于ab不等于1,两边约去ab-1,得：5(ab+1)+2001b=0----(4)
即2001b=-5(ab+1)
(2)两边乘以a^2,得：5a^2+2001ba^2+9a^2b^2=0----(5)
用(5)-(1),得：9(a^2b^2-1)+2001a(ab-1)=0,两边约去ab-1,得：9(ab+1)+2001a=0----(6)
即2001a=-9(ab+1)
所以a/b=2001a/(2001b)=9/5