m^2+m-1=0,求m^3+2m^2+2013

来源：学生学帮网编辑：学帮网时间：2024/06/25 12:59:38

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

m²＋m＝1
m³＋2m²＋2013
＝m³＋m²＋m²＋2013
＝m﹙m²＋m﹚＋m²＋2013
＝m＋m²＋2013
＝1＋2013
＝2014.

∵m²+m-1=0
∴m²+m=1
∴m³+2m²+2013=m(m²+m)+m²+2013=m+m²+2013=1+2013=2014