已知m是方程x²+x-1=0的根,求m³+2m²+2007的值

已知m是方程x²+x-1=0的根,求m³+2m²+2007的值
已知m是方程x²+x-1=0的根,求m³+2m²+2007的值

已知m是方程x²+x-1=0的根,求m³+2m²+2007的值
解由m是方程x²+x-1=0的根
得m^2+m-1=0
即m^2+m=1
故由m^3+2m^2+2007
=m^3+m^2+m^2+2007
=m（m^2+m）+m^2+2007
=m+m^2+2007
=m^2+m+2007
=1+2007
=2008