已知a2-a-1=0,则a3-2a+2011=_.
问题描述:
已知a2-a-1=0,则a3-2a+2011=______.
答
∵a2-a-1=0,
∴a2=a+1.
∵a3-2a+2011=a3-a-a-1+2012,
∴a3-2a+2011=a(a2-1)-(a+1)+2012
=a(a+1-1)-a2+2012
=2012.
故答案为:2012.