若m²+m-1=0,求m³+2m²+2008的值

若m²+m-1=0,求m³+2m²+2008的值

∵m²+m-1=0
∴m²=1-m
∴m³+2m²+2008
=m(1-m)+2m²+2008
=m²+m+2008
=1+2008
=2009

误解

无解

等式两边者都乘以（m+1）
（m²+m-1）*（m+1)=0
m^3+m^2-m+m^2+m-1=0
m^3+2m^2=1
所以：m³+2m²+2008=1+2008=2009