分析:∵x13=x1x12=x1(1-x1)=x1-x12=2x1-1-2x22=-2(1-x2)=-2+2x2,所以x13-2x22+2008=2x1-1-2+2x2+2008=2003.
解答:解:∵x1,x2是方程x2+x-1=0的兩個實數(shù)根,
∴x1+x2=-1;
又∵x13=x1x12
=x1(1-x1)
=x1-x12
=2x1-1-2x22
=-2(1-x2)
=-2+2x2,
∴x13-2x22+2008
=2x1-1-2+2x2+2008
=2(x1+x2)+2005
=-2+2005
=2003.
故答案為:2003.
點評:此題主要考查了根與系數(shù)的關系、代數(shù)式的求值.將根與系數(shù)的關系與代數(shù)式變形相結(jié)合解題是一種經(jīng)常使用的解題方法.