math 恒等式

唔該睇一睇第三題有冇打錯野?

2009-02-03 21:45:39 補充：
左邊會唔會係7X/(9-X^2)?

2009-02-05 10:13:26 補充：
1. A-2B = 3 ---(1)
3A-B = 4 ---(2)
(2)*2: 6A-2B = 8 ---(3)
(3)-(1): 5A = 5
A = 1
將 A = 1 代入 (1):
1-2B = 3
2B = -2
B = -1
2. X(X+A)-B(X+2) = X(X-3)+A
X^2+AX-BX-2B = X^2-3X+A
X^2+(A-B)X-2B = X^2-3X+A
A-B = -3 ---(1)
-2B = A ---(2)
將 (2) 代入 (1):
-2B-B = -3
-3B = -3
B = 1
將 B = 1 代入 (2):
A = -2(1) = -2
3. (7X+9)/(X^2-9) = A/(X+3)+B/(X-3)
(7X+9)/[(X+3)(X-3)] = [A(X-3)+B(X+3)]/[(X+3)(X-3)]
7X+9 = AX-3A+BX+3B
7X+9 = (A+B)X-3A+3B
A+B = 7 ---(1)
-3A+3B = 9 ---(2)
(2)/3: -A+B = 3 ---(3)
(1)+(3): 2B = 10
B = 5
(1)-(3): 2A = 4
A = 2
4. 8x/(x^2+2x-3) = a/(x+3)-b/(x-1)
8x/[(x+3)(x-1)] = [a(x-1)-b(x+3)]/[(x+3)(x-1)]
8x = ax-a-bx-3b
8x = (a-b)x-a-3b
a-b = 8 ---(1)
-a-3b = 0 ---(2)
(1)+(2): -4b = 8
b = -2
將 b = -2 代入 (1):
a-(-2) = 8
a+2 = 8
a = 6

1) 若 (A-2B)X+3A-B≡3X+4 , 求A和B的值
比較左方和右方同類項可得,
A-2B=3_______________(1)
3A-B=4_______________(2)
(2)-(1)x3:
5B=-5
B=-1
把B=-1代入(2)
3A-(-1)=4
A=1

2009-02-03 22:06:10 補充：
2) X(X+A) -B(X+2)≡X(X-3)+A , 求A和B的值
左方= X^2 +AX -BX-2B
=X^2 +(A-B)X-2B
右方=X(X-3)+A
=X^2 -3X+A
比較左方和右方同類項,可得
A-B=-3_________________(1)
-2B=A__________________(2)
把(2)代入(1)
-2B-B=-3
-3B=-3
B=1
把B=1代入(2)
A=-2