Question

若m是方程x2+x-1=0的根，则式子m三次方+2m2+2013的值为

Answer 1

因为m²+m=1
所以m³+2m²+2013
=m（m²+2m）+2013
=m（m²+m+m）+2013
=m（1+m）+2013
=m²+m+2013
=1+2013
=2014

Answer 2

m²+m-1=0
m³+2m²+2013
=m²(m+1)+2013
=(1-m)(1+m)+2013
=1-m²+2013
=2013+m
m=(1±√5)/2
代入即可