设m^2 + m =1,求m^3 + 2m^2 +2005的值

问题描述:

设m^2 + m =1,求m^3 + 2m^2 +2005的值

m²+m=1所以m²=1-mm³+2m²+2005=m(m²)+2m²+2005=m(1-m)+2m²+2005=m-m²+2m²+2005=m+m²+2005=(m²+m)+2005=1+2005=2006