恆等式f4(急!!20點)

A+B(x+1)+C(x+1)^2=3x^2-9x+1

when x = -1 :

A = 3+9+1 = 13

when x = 0 :

13 + B + C = 1

B + C = - 12....(1)

when x = - 2 :

13 - B + C = 12 + 18 + 1

B - C = - 18....(2)

(1) + (2) :

2B = - 12 - 18

B = - 15

C = - 12 - (-15) = 3


2009-12-24 14:50:19 補充：
如答案是A=-5,B=-3,C=3

LHS = -5 -3(x+1) + 3(x+1)^2

= -5 -3x-3 + 3x^2+6x+3

= 3x^2 + 3x - 5 不等如RHS的

你的答案是錯了。

2009-12-24 15:45:48 補充：
不緊要,再做一次 :

A+B(x-1)+C(x-1)^2=3x^2-9x+1

when x = 1 :

A = 3-9+1 = - 5

when x = 0 :

- 5 - B + C = 1

B - C = - 6......(1)

when x = 2 :

- 5 + B + C = 12-18+1

B + C = 0..........(2)

(1)+(2) : 2B = -6

B = - 3

C = 3

是答案有錯吧!~~~