设m²+m=1,求m³+2m²+2009的值

网友回答

m²+m=1
所以m³+2m²
=m³+m²+m²
=m(m²+m)+m²
=m+m²
=1所以原式=1+2009=2010
======以下答案可供参考======
供参考答案1:
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供参考答案2:
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