已知m2+m-1=0,那么m³+2m²+2012=?

已知m2+m-1=0,那么m³+2m²+2012=?
已知m2+m-1=0,那么m³+2m²+2012=?

已知m2+m-1=0,那么m³+2m²+2012=?
m2+m-1=0
m²+m=1
m³+2m²+2012
=m³+m²+m²+2012
=m(m²+m)+m²+2012
=m+m²+2012
=1+2012
=2013

m²+m=1
所以m³+2m²
=m³+m²+m²
=m(m²+m)+m²
=m+m²
=1
所以原式=1+2012=2013

因为m^2+m-1=0
所以m^2+m=1
所以m^3+2m^2+2012=m(m^2+m)+m^2+2012
=m+m^2+2012
=1+2012
=2013

m²+m-1=0 可得：m²+m=1
m³+2m²+2012
=(m³+m²)+m²+2012
=m(m²+m)+m²+2012
=m+m²+2012
=1+2012
=2013

根据已知得m²+m=1

m³+2m²+2012=m³+m²+m²+2012=m（m²+m）+m²+2012=m+m²+2012=1+2012=2013