若m²+m-1=0,求m³+2m²+2011的值

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若m²+m-1=0,求m³+2m²+2011的值
若m²+m-1=0,求m³+2m²+2011的值

若m²+m-1=0,求m³+2m²+2011的值
因为m²+m-1=0
所以 m²+m=1
m³+2m²+2011
=m³+m²+m²+2011
=m(m²+1)+m²+2011
=m+m²+2011
=1+2011
=2012

m³+2m²+2011
=m³+m²-m+m²+m-1+2012
=m²(m²+m-1)+(m²+m-1)+2012
=2012