Question

若m是方程x²+x-1=0的一个根,试求代数式m³+2m²+2012的值

Answer 1

x=m
m²+m-1=0
m²+m=1
所以m³+2m²
=m³+m²+m²
=m(m²+m)+m²
=m+m²
=1
所以原式=2013