已知m²+m-1=0,则代数式m³+2m²+2009的值

已知m²+m-1=0,则代数式m³+2m²+2009的值
已知m²+m-1=0,则代数式m³+2m²+2009的值

已知m²+m-1=0,则代数式m³+2m²+2009的值
m²+m-1=0
两边同*m,得
m³+m²-m=0
m³+2m²+2009=(m³+m²-m)+m²+m+2009
=m²+m+2009
=1+2009
=2010

m²+m-1=0
m²+m=1
m³+2m²+2009
=m(m²+m+m)+2009
=m(1+m)+2009
=m²+m+2009
=2010

m³+2m²+2009
=m(m²+m-1)+m²+m+2009
=m(m²+m-1)+(m²+m-1)+2010
=0+0+2010
=2010