若m2次方+m-1=0,求m3次方+2m2次方+2008的值.

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

若m2次方+m-1=0,求m3次方+2m2次方+2008的值.
m²+m-1=0
m²+m=1
m^3+m²=m
m^3+2m²+2008
=m²+m+2008
=1+2008
=2009

你好，过程如下
由题知道 m^2+m=1
原式子= m^3+2m^2+2008
= m^3+m^2+m^2+2008
=m(m^2+m)+m^2+2008
=m+m^2+2008
=1+2008
=2009

m^2+m-1=0 => m^2=1-m
m^3+2m^2+2008=(m+1)m^2+m^2+2008
=(1+m)*(1-m)+m^2+2008
=1-m^2+m^2+2008=2009
OK!