设m²+m=1,求m³+2m²+2009的值

设m²+m=1,求m³+2m²+2009的值
设m²+m=1,求m³+2m²+2009的值

设m²+m=1,求m³+2m²+2009的值
m²+m=1
所以m³+2m²
=m³+m²+m²
=m(m²+m)+m²
=m+m²
=1
所以原式=1+2009=2010

m(m+1)=1 所以m+1=1/m

所以m³+2m²+2009
=m²（m+1+1）+2009
=m²（1/m+1）+2009
=m²+m+2009
=1+2009
=2010

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