已知m^2+m-1=0,求代数式m^3+2m^2+2004的值

题目

已知m^2+m-1=0,求代数式m^3+2m^2+2004的值

答案

m²+m-1=0
m^3+m²-m=0
m^3+2m²-m-m²=0
m^3+2m²=m²+m
所以,m^3+2m²+2004=m²+m+2004=1+2004=2005