∵a是方程x² +x-1=0的根
∴a²+a-1=0
∴2000a³ +4000a²
=2000a³+2000a²-2000a+2000a²+2000a-2000+2000
=2000a(a²+a-1)+2000(a²+a-1)+2000
∵a²+a-1=0
∴原式=2000a×0 +2000×0+2000
=2000