Question

已知m^2+m-1=0,试求代数式m^3+2m^2+2000的值.

要详细的解答过程......
要将复杂问题简单化...

Answer 1

m^2+m-1=0所以m^2+m=1所以m^3+m^2＝m
代数式m^3+2m^2+2000
＝m^3+m^2+m^2+2000
=m+m^2+2000
=1+2000
=2001

Answer 2

m^2+m-1=0所以m^2+m=1所以m^3+m^2＝m
代数式m^3+2m^2+2000
＝m^3+m^2+m^2+2000
=m+m^2+2000
=1+2000
=2001

Answer 3

这题的方程不难，建议用代数法，解出二次方程的两个根，然后分别带入3次代数式里面

Answer 4

m^2+m-1=0 --> m^2+2m+1=m+2 --> (m+1)^2=m+2 -->
m*((m+1)^2)=m*(m+2)

m^3+2m^2+2000 = m^3+2m^2+m-m+2000 = m*((m+1)^2)-m+2000 = m*(m+2)-m+2000 = m^2+2m-m+2000 = m^2+m+2000 = 2001

Answer 5

解：由已知，m^2+m-1=0
可得： m^2+m=1
m^3+2m^2+2000
=m^3+m^2+m^2+2000
=m(m^2+m)+m^2+2000
=m+m^2+2000
=2001