已知m^2+m-1=0,那么m^4+2m^3-m-2009=

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已知m^2+m-1=0,那么m^4+2m^3-m-2009=
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已知m^2+m-1=0,那么m^4+2m^3-m-2009=
已知m^2+m-1=0,那么m^4+2m^3-m-2009=

已知m^2+m-1=0,那么m^4+2m^3-m-2009=
由m^2+m-1=0得,m^2+m=1
(m^2+m)^2=m^4+2m^3+m^2
所以m^4+2m^3-m-2009
=(m^2+m)^2-m^2-m-2009
=(m^2+m)^2-(m^2+m)-2009
=1-1-2009
=-2009

由m^2+m-1=0得m^2+m=1
m^4+2m^3-m-2009
=(m^4+m^3)+m^3-m-2009
=m^2(m^2+m)+m^3-m-2009
=m^2+m^3-m-2009
=m(m^2+m)-m-2009
=m-m-2009
=-2009