若m²+m-1=0,求m³+2×m²+2009等于什么
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若m²+m-1=0,求m³+2×m²+2009等于什么
若m²+m-1=0,求m³+2×m²+2009等于什么
若m²+m-1=0,求m³+2×m²+2009等于什么
因为 m²+m-1=0--------
所以,m²=1-m,m=1-m²---
m³+2×m²+2009=m²*m+2×m²+2009
=m²*(m+2)+2009
=(1-m)*(m+2)+2009
=m+2-m²-2m+2009
=[(1-m²)-m]+2010 -----------上面有这个m=1-m²---
=2010
----------------------------------------------------------------OK啦---------------------------------
m²+m-1=0,
可得m(m+1)=1
由m³+2×m²+2009=m(m+1)(m+1)-m+2009
把m(m+1)=1代入上式可得
=(m+1)-m+2009
=2010
2010