已知m²+m-1=0,求m³+2m²+2012的值

已知m²+m-1=0,求m³+2m²+2012的值
已知m²+m-1=0,求m³+2m²+2012的值

已知m²+m-1=0,求m³+2m²+2012的值
由m²+m-1=0
得m²+m=1
m³+2m²+2012
=m³+m²+m²+2012
=m(m²+m)+m²+2012
=m·1+m²+2012
=m²+m+2012
=1+2012
=2013
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答案是2013，
由已知易得m²+m=1
则m³+2m²+2012=m³+m²+m²+2012=m(m²+m)+m²+2012=m+m²+2012=1+2012=2013

m²+m-1=0
两边同时乘以m,得m³+m²-m=0
m³+m²=m
m³+2m²+2012=m³+m²+m²+2012
=m+m²+2012=1
+2012=2013

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