已知m²+m-1=0,求m³+2m²+2004的值

已知m²+m-1=0,求m³+2m²+2004的值
已知m²+m-1=0,求m³+2m²+2004的值

已知m²+m-1=0,求m³+2m²+2004的值
m³+2m²+2004
=m(m²+m-1)+m²+m+2004
=m(m²+m-1)+(m²+m-1)+2005
=0+0+2005
=2005
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∵m²+m-1=0
∴m²+m=1
m³+2m²+2004
=m（m²+m）+m²+2004
=m×1+m²+2004
=1+2004
=2005

m³+2m²+2004
= m(m²+m-1) + m²+m+2004
= 0 + m²+m-1 + 2005
= 2005