已知m^2+m-1=0,求代数式m^3+5m^2+3m-2012的值

问题描述:

已知m^2+m-1=0,求代数式m^3+5m^2+3m-2012的值

m^2+m-1=0
m^2+m=1
m^3+5m^2+3m-2012 =m(m^2+5m+3)-2012
=m(m^2+m+4m+3)-2012
=m(1+4m+3)-2012
=4(m^2+m)-2012
=4-2012
= - 2008