m^2+m-1=0,求m^3+2m^2+2008的值

m^2+m-1=0,求m^3+2m^2+2008的值
m^2+m-1=0,求m^3+2m^2+2008的值

m^2+m-1=0,求m^3+2m^2+2008的值
m^2+m=1
m^2+2m=1+m
m^3+2m^2+2008
=m(m^2+2m)+2008
=m(1+m)+2008
=m^2+m+2008
=1+2008
=2009

2009 遇到这种题目不要盲目解 一年级三元算是难的 肯定是由条件引入！注意条件

m^3+2m^2+2008
=m(m^2+m)+m^2+2008
=m+m^2+2008
=2009
就是不断把条件代入

m^2+m=1 (已知)
m^2+2m=1+m
m^3+2m^2+2008
=m(m^2+2m)+2008
=m(1+m)+2008
=m^2+m+2008
=1+2008
=2009

∵m^2+m-1=0
∴m^2+m=1
即m^2+2m=1+m
得m^3+2m^2+2008
=m(m^2+2m)+2008
=m(1+m)+2008
=（m^2+m）+2008
=1+2008
=2009