若m的平方+m-1=0,求m的立方+2 (m的立方)+2008的值

问题描述:

若m的平方+m-1=0,求m的立方+2 (m的立方)+2008的值
答案是2009,

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