已知m^2+m-1=0,求m^3+2m^2+1997的值.不要太多,简短点,只要有关键的过程.

来源：学生作业帮助网编辑：作业帮时间：2024/11/14 02:06:47

已知m^2+m-1=0,求m^3+2m^2+1997的值.不要太多,简短点,只要有关键的过程.
已知m^2+m-1=0,求m^3+2m^2+1997的值.
不要太多,简短点,只要有关键的过程.

已知m^2+m-1=0,求m^3+2m^2+1997的值.不要太多,简短点,只要有关键的过程.
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

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

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

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

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

已知m*m+m-1=0,求m*m*m+2m*m-2005 已知m²+2m+1=0,求m³+2m²+3m 已知m-1/m=3,m不等于0,求m^2-1/m^2,m^3-1/m^3,m^4-1/m^4 已知m^2-5m+1=0,求m^3+1/m^3 和m-1/m的值已知m^2-3m-1=0,求m^2-1/m^2 已知m^2+m-1=0求m^3+2m^2+2015的值已知m^2-m-1=0,求-m^3+2m^2+2009的值已知m^2+m-1=0,求m^3+2m^2-2005的值如题已知m^+m-1=0,求m^3+2m^2-2009=? 已知m^2-m-1=0 求代数式m^3-2m+2005 已知m²+m-1=0,求m³+2m²+3的值已知m^2+m-1=0,求m^3+2m-1997的值.[提示：m^3+2m^2-1997=(m^3+m^2-m)+(m^2+m-1)-1996] 已知m^2+m-2=0 求m^3+2m^2-m+1的值已知m^2+m-1=0,求m^3+2m^2+3m的值. 已知m^2-5m-1=0,求3m^2-10m+1/m^2 已知m^2-3m-1=0 求m^3-m^2-7m+2008的值已知m^2+m-1=0,求代数式m^3+5m^2+3m-2012的值已知m^2+m-1=0,求m^3+5m^2+3m-2009的值.