已知m²+m-1=0,求代数式m³+2m²+2010的值

已知m²+m-1=0,求代数式m³+2m²+2010的值
已知m²+m-1=0,求代数式m³+2m²+2010的值

已知m²+m-1=0,求代数式m³+2m²+2010的值
因为m²+m-1=0,所以m²+m=1.
m³+2m²+2010
=m³+m²+m²+2010
=m（m²+m）+m²+2010
=m+m²+2010
=2011

m²+m-1=0
m²+m=1
m³+2m²+2010
=m(m²+m+m)+2010
=m(1+m)+2010
=m²+m+2010
=1+2010
=2011

这是一道因式分解的题
m³+2m²+2010=m³+m²+m²+2010
=m³+m²+m²-m+m+2010
=(m³+m²-m)+(m²+m-1)+2011
=m(m²+m-1)+(m²+m-1)+2011
=(m²+m-1)(m+1)+2011
∵m²+m-1=0
∴m³+2m²+2010=2011