已知x2-x-1=0,则-x3+2x2+2008的值为?

问题描述:

已知x2-x-1=0,则-x3+2x2+2008的值为?

已知x²-x-1=0,那么:x²-x=1,x²=x+1
所以:
-x³+2x²+2008
=-x²·x+ 2x²+2008
=-(x+1)·x+ 2x²+2008
=-x²-x+2x²+2008
=x²-x+2008
=1+2008
=2009