设m^2+m－2=0,求m^3+3m^2+2000的值要过程,谢谢

设m^2+m－2=0,求m^3+3m^2+2000的值要过程,谢谢
设m^2+m－2=0,求m^3+3m^2+2000的值
要过程,谢谢

设m^2+m－2=0,求m^3+3m^2+2000的值要过程,谢谢
m^2+m－2=0 (1)
m^3+m^2－2m=0 (2)
(2)+(1)+(1)
m^3+3m^2-4=0
m^3+3m^2+2000=2004
楼上m=1算错了

m^2+m-2=0
(m+2)*(m-1)=0
m=-2 或 m=1
代入可得
m^3+3m^2+2000= - 2^3+3*(-2)^2+2000=2004
或 m^3+3m^2+2000=1+3+2000=2004

方法一：
m^2+m－2=0 ====>
m = -2 , or m = 1
m = 1 时， m^3+3m^2+2000 = 2004
m = -2 时，m^3+3m^2+2000 = 2004
所以，m^3+3m^2+2000 = 2004
方法二：
m^3+3m^2+2000 = m^3 + m^2 - 2m + 2m^2 + 2m - 4 + 2004 =
m(m^2 + m - 2) + 2(m^2 + m - 2) + 2004 =
2004