已知,m²+m-1=0,则m³+2m²-2007的值是

已知,m²+m-1=0,则m³+2m²-2007的值是
已知,m²+m-1=0,则m³+2m²-2007的值是

已知,m²+m-1=0,则m³+2m²-2007的值是
由题意得
m²+m=1
m³+2m²-2007
=m【m²+m+m】-2007
=m【m+1】-2007
=m²+m-2007
=1-2007
=-2006

m^3+2m^2-2007=m(m^2+m-1)+m^2+m-2007=m^2+m-2007.又由已知可推出m^2+m=1所以答案是-2006.

∵m²+m-1=0，
∴m²+m=1
则m³+2m²-2007
=m³+m²+m²-2007
=m(m²+m)+m²-2007
=m+m²-2007
=1-2007
=-2006
希望能采纳