已知m^2 +m -1=0,求m^3+2m^2+2007的值 求过程和解释
问题描述：
已知m^2 +m -1=0,求m^3+2m^2+2007的值 求过程和解释
答
m^2 +m -1=0
m^2 +m=1
m^3+2m^2+2007
=m^3+m^2+m^2+2007
=m(m^2+m)+m^2+2007
=m+m^2+2007
=1+2007
=2008
答
m^2 +m -1=0,
m^2+m=1
m^3+2m^2+2007
=m*(m^2+m+m)+2007
=m*(1+m)+2007
=m^2+m+2007
=1+2007
=2008
答
因为 m^2 +m -1=0,所以 m^2 +m=1
将 m^2 +m=1 左右两边都乘以 m,得到 m^3+m^2=m,左右两边同时加上m^2,得到
m^3+2m^2=m^2+m,所以 m^3+2m^2=1
所以 m^3+2m^2+2007=1+2007=2008