m^2+m-1=0,求m^3+2m^2+2013

来源：学生作业帮助网编辑：作业帮时间：2024/05/04 12:44:14

m^2+m-1=0,求m^3+2m^2+2013
m^2+m-1=0,求m^3+2m^2+2013

m^2+m-1=0,求m^3+2m^2+2013
m^2+m-1=0
m^2+m=1
m^3+2m^2+2013
=m^3+m^2+m^2+2013
=m(m^2+m)+m^2+2013
=m+m^2+2013
=1+2013
=2014

m^3+2m^2+2013
=m³+m²-m+m²+m-1+2014
=m(m²+m-1)+(m²+m-1)+2014
=0+0+2014
=2014

m²＋m=1
则：
m³＋2m²＋2013
=(m³＋m²)＋m²＋2013
=m(m²＋m)＋m²＋2013
=m＋m²＋2013
=1＋2013
=2014

m^2+m-1=0
m^2+m=1
m^3+2m^2+2013
=m^3+m^2+m^2+2013
=m(m^2+m)+m^2+2013
=m+m^2+2013
=1+2013
=2014

m^2+m-1=0
m^2=-m+1
m^3+2m^2+2013
=m^2(m+2)+2013
=(-m+1)(m+2)+2013
=-m^2-m+2+2013
=-1+2015
=2014