Question

已知m是方程x²+x-1=0的根,求m³+2m²+2007的值

Answer 1

解由m是方程x²+x-1=0的根

得m^2+m-1=0

即m^2+m=1

故由m^3+2m^2+2007

=m^3+m^2+m^2+2007

=m（m^2+m）+m^2+2007

=m+m^2+2007

=m^2+m+2007

=1+2007

=2008