Maths Question
2008-09-05 11:46 pm
1. Find the values of the constants A and B in the following identity.
Ax(x-1) + B(x-1)(x+1) 三 -x2 - x + 2
回答 (2)
2008-09-07 12:34 am
✔ 最佳答案
Ax(x-1) + B(x-1)(x+1) 三 -x2 - x + 2L.H.S.= Ax2-Ax+B(x2-1)
= Ax2-Ax+Bx2-B
=Ax2+Bx2-Ax-B
R.H.S.=-x2 - x + 2
By comparing the coefficient of like terms, we have
-B=+2
B=-2
-A=-1
A=1
2008-09-06 12:37 am
Ax(x-1) + B(x-1)(x+1)
= Ax^2 - Ax + B(x^2-1^2)
= Ax^2 - Ax + Bx^2 - B
= (A + B)x^2 - Ax - B
比較(A + B)x^2 - Ax - B 三 -x2 - x + 2
- A = - 1
A = 1
- B = 2
B = - 2
L.H.S. = (A + B) 代A = 1, B = - 2
= 1 - 2 = -1 = R.H.S.
∴ A = 1, B = - 2
= Ax^2 - Ax + B(x^2-1^2)
= Ax^2 - Ax + Bx^2 - B
= (A + B)x^2 - Ax - B
比較(A + B)x^2 - Ax - B 三 -x2 - x + 2
- A = - 1
A = 1
- B = 2
B = - 2
L.H.S. = (A + B) 代A = 1, B = - 2
= 1 - 2 = -1 = R.H.S.
∴ A = 1, B = - 2
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