已知m^2+m-1=0,则m^3++2m^2+2011=

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已知m^2+m-1=0,则m^3++2m^2+2011=
已知m^2+m-1=0,则m^3++2m^2+2011=

已知m^2+m-1=0,则m^3++2m^2+2011=
m^2+m-1=0 m^2+m=1
m^3+2m^2+2011
=m(m^2+m+m)+2010
=m(1+m)+2011
=(m^2+m)+2011
=1+2011
=2012

m^3+2m^2+2011
=m(m²+m-1)+m²+m-1+2012
=0+0+2012
=2012

m²+m-1=0
m²+m=1
所以原式=m³+m²+m²+2011
=m(m²+m)+m²+2011
=m+m²+2011
=1+2011
=2012

m^3+2m^2+2011
=m^3+m^2-m+m^2+m-1+2012
=m(m^2+m-1)+m^2+m-1+2012
=2022

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