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.

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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

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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

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