急...中2數學

2007-09-02 11:13 pm
求未知常數A和B的值

1) 3(4x-8)≡4(Ax+B)

2) 2Ax^2+A×+B×+3≡4x^2-x+3

3) (Ax+2)(3-x)≡-x^2+Bx+6

4) (x+1)(2x-3)≡2x^2+Ax+B

回答 (2)

2007-09-02 11:28 pm
✔ 最佳答案
1)
LHS=3(4x-8)
=12x-24
=4(3x-6)
RHS=4(Ax+B)
A=3,B=-6
2)
2Ax^2=4x^2
A=2
x(A+B)=-x
A+B=-1
2+B=-1
B=-3
3)
LHS=3Ax+6-Ax^2-2x
=-Ax^2+x(3A-2)+6
-A=-1
A=1
3A-2=B
3-2=B
B=1
4)
LHS=2x^2+2x-3x-3
=2x^2-x-3
A=-1
B=-3
參考: me
2007-09-02 11:29 pm
1)
LHS = 12x - 24
RHS = 4Ax + 4B
4A = 12--------------(1)
4B = -24------------------(2)
From (1) and (2)
A = 3
B = -6

2)
LHS = 2A x^2 + (A + B)x + 3
RHS = 4 x^2 - x + 3
2A = 4-----------(1)
A + B = -1 --------------(2)
From (1) , A = 2
Substitute A = 2 into (2)
2 + B = -1
B = -3

3)
LHS = (Ax+2)(3-x)
= 3Ax + 6 - A x^2 - 2x
= -A x^2 + (3A - 2)x + 6
RHS = -x^2+Bx+6
A = -1
3A - 2 = B --------------(1)
From (1)
-3 - 2 = B
B = -5

4)
LHS = (x+1)(2x-3)
= 2 x^2 + 2x - 3x - 3
= 2 x^2 - x - 3
RHS = 2x^2+Ax+B
A = -1
B = -3


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