x2-x-1=0,则2x3+7x2-11x+2012=_.
问题描述:
x2-x-1=0,则2x3+7x2-11x+2012=______.
答
∵x2-x-1=0,
∴x2-x=1,
∴2x3+7x2-11x+2012
=2x(x2-x)+9x2-11x+2012
=9x2-9x+2012
=9(x2-x)+2012
=9+2012
=2021.
故答案是:2021.