Question

已知m^2+m-1=0,求m^3+2m^2+1997的值.

数学题，求过程，不要太多，简短点，只要有关键的过程。

Answer 1

你好
m^2+m-1=0
得m²+m=1
m^3+2m^2+1997
=m(m²+m)+m²+1997
=m×1+m²+1997
=m²+m+1997
将上m²+m=1
带入得1998

Answer 2

m²+m-1=0
m²+m=1

m^3+2m^2+1997
=m（m²+m）+m²+1997
=m+m²+1997
=1+1997
=1998

如有不明白，可以追问
如有帮助，记得采纳，谢谢

Answer 3

m^2+m-1=0
m²+m=1
∴m^3+2m^2+1997
=m(m²+m)+m²+1997
=m×1+m²+1997
=m²+m+1997
=1+1997
=1998

Answer 4

m^2+m-1=0
m^2+m=1
m^3+2m^2+1997
=m^3+m^2+m^2+1997
=m(m^2+m)+m^2+1997
=m+m^2+1997
=1+1997
=1998

Answer 5

m^3+2m^2+1997=m（m^2+m）+m^2+1997=m*1+m^2+1997=1+1997=1998