Question

已知m²+m=1，那么m³+2m²-2014的值为？

初中数学问题

Answer 1

 

已知m²+m=1，那么m³+2m²-2014的值

Answer 2

m³+2m²-2014
=m³-1+2m²-2-2011
=(m-1)(m²+m+1)+2(m²-1)-2011
因为m²+m=1,所以m²-1=m,m-1=m²
(m-1)(m²+m+1)+2(m²-1)-2011
=2m²+2m-2011
=2(m²+m)-2011
=2-2011
=2009

Answer 3

m²=1-mm³+2m²=m(1-m)+2(1-m)=2-(m²+m)=1
m³+2m²-2014=1-2014=-2013

Answer 4

∵m²+m=1
∴m²+m-1=0
m³+2m²-2014
=m³+m²-m+m²+m-1-2013
=m(m²+m-1)+(m²+m-1)-2013
∵m²+m-1=0
∴原式=0+0-2013=-2013

追问

求每一步的解题思路，详细解释。