设m²+m=1,求m³+2m²+2009的值
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![设m²+m=1,求m³+2m²+2009的值](/uploads/image/z/1693877-5-7.jpg?t=%E8%AE%BEm%26%23178%3B%2Bm%3D1%2C%E6%B1%82m%26%23179%3B%2B2m%26%23178%3B%2B2009%E7%9A%84%E5%80%BC)
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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