已知m2+m-1=0,求m3+2m2-2005的值?

来源：百度知道 编辑：UC知道 时间：2024/06/01 05:43:42
2代表平方,3代表立方

m²+m-1=0
m²=1-m

m³+2m²-2005
=m²(m+2)-2005
=(1-m)(m+2)-2005
=-m²-m+2-2005
=m-1-m-2003
=-2004

由：m^2+m-1=0

得：m^2+m=1

m^3+2m^2-2005

=m^3-1+2m^2-2004
=(m-1)(m^2+m+1)+2m^2-2004
=(m-1)(1+1)+2m^2-2004

=2(m-1)+2m^2-2004
=2m-2+2m^2-2004

=2(m^2+m)-2006
=2*1-2006

=2004

m3+2m2-2005
=m(m2+m-1)+m2+m-2005
=m(m2+m-1)+(m2+m-1)-2004
=m*0+0-2004
+-2004

mm+m=1
mmm+mm=m
mmm+2mm-2005
=mmm+mm+mm+m-m-2005
=m+1-m-2005
=-2004

m3+2m2-2005=m(m2+m-1)+m2+m-1-2004
因为m2+m-1=0
所以m(m2+m-1)+m2+m-1-2004=-2004

m^2+m-1=0 m^2=1-m,m^2+m==1
m^3+2m^2-2005=m^2(m+2)-2005=(1-m)(m+2)-2005=2-m^2-m-2005=2-1-2005=-2004