若m²+m-1=0,求m³+2m²+2008的值

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/23 06:54:49
若m²+m-1=0,求m³+2m²+2008的值若m²+m-1=0,求m³+2m²+2008的值若m²+m-1=0,求m³

若m²+m-1=0,求m³+2m²+2008的值
若m²+m-1=0,求m³+2m²+2008的值

若m²+m-1=0,求m³+2m²+2008的值

∵m²+m-1=0
∴m²=1-m
∴m³+2m²+2008
=m(1-m)+2m²+2008
=m²+m+2008
=1+2008
=2009

误解

无解

等式两边者都乘以(m+1)
(m²+m-1)*(m+1)=0
m^3+m^2-m+m^2+m-1=0
m^3+2m^2=1
所以:m³+2m²+2008=1+2008=2009