m^2+m-1=0 求m^3+2m^2+2008=?速求

m^2+m-1=0 求m^3+2m^2+2008=?速求
m^2+m-1=0 求m^3+2m^2+2008=?
速求

m^2+m-1=0 求m^3+2m^2+2008=?速求
m^2+m=1 m^3+2m^2+2008
m^2+m+m=1+m =m(m^2+2m)+2008
m^2+2m=1+m =m(1+m)+2008
=m^2+m+2008
=1+2008
=2009

若m^2+m-1=0,求m^3+2m^2+2008
因m^2+m-1=0
所以m^3+m^2-m=0
m^3+2m^2+2008=m-m^2+2m^2+2008=m+m^2+2008=2009

m^3+2m^2+2008
=m^3+m^2+m^2+m-m+2008
=m^3+m^2-m+m^2+m+2008
因m^2+m-1=0 所以m^3+m^2-m=0 ，m^2+m=1
所以原式=0+ 1+2008
=2009