已知m²+m-1=0,求m³+2m²-2005

问题描述：

答

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

答

由题知：m²+m=1
∴原式=m(m²+m）+m²-2005
=m+m²-2005
=1-2005
=-2004
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答

m³+2m²=1

答

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

答

很高兴回答你的问题∵m²+m-1=0∴m²+m=1m³+2m²-2005=m³+m²+m²-2005=m(m²+m)+m²-2005=m·1+m²-2005=m²+m-2005=1-2005=-2004