若a是方程x² x-1=0的根,求代数式2000a³ 4000a²的值x²+x-1,2000a³+4000a²

若a是方程x² x-1=0的根,求代数式2000a³ 4000a²的值x²+x-1,2000a³+4000a²
若a是方程x² x-1=0的根,求代数式2000a³ 4000a²的值
x²+x-1,2000a³+4000a²

若a是方程x² x-1=0的根,求代数式2000a³ 4000a²的值x²+x-1,2000a³+4000a²
∵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

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