已知x2-x-1=0,求多项式-x3+2x2+2011的值.

问题描述:

已知x2-x-1=0,求多项式-x3+2x2+2011的值.

∵x2-x-1=0,
∴x2-x=1,
∴-x3+2x2+2011
=-x3+x2+x2+2011
=-x(x2-x)+x2+2011
=-x+x2+2011
=1+2011
=2012.