已知x2+x-1=0,则代数式x3+2x2+2008的值为_.

问题描述:

已知x2+x-1=0,则代数式x3+2x2+2008的值为______.

∵x2+x-1=0,∴x2+x=1,
x3+2x2+2008,
=x(x2+x)+x2+2008,
=x+x2+2008,
=2009,
当x2+x=1时,原式=2009.
故答案为:2009.