F.2 Maths

1. if 3(x-2)+2(A-2x) identity to Bx-4, where A and B are constants, find A and B.

3(x-2)+2(A-2x) = Bx-4
3x-6+2A-4x = Bx-4
2A-6 -3x = Bx-4
coefficients on each side is equal...
2A-6=-4 and -3=B
2A = 4/6 and B=-3
A = 1/3 and B = -3

2. If (x+4)(2x-A) identity to Bx^2 + 5x + C, where A, B and C are constants, find A, B and C.

(x+4)(2x-A) = Bx^2 + 5x + C
8x^2 + 8x - Ax - 4A = Bx^2 + 5x + C
8x^2 + (8 - A)x - 4A = Bx^2 + 5x + C
B=8, 8-A=5, -4A=C
B=8, A= 8-5=3, C=-4(3)=-12

2007-03-02 22:14:05 補充：
唔好意思 1 計錯數3(x-2) 2(A-2x) = Bx-43x-6 2A-4x = Bx-42A-6 -x = Bx-4

2007-03-02 22:14:40 補充：
唔好意思 1 計錯數3(x-2) 2(A-2x) = Bx-43x-6 2A-4x = Bx-42A-6 -x = Bx-4 l.h.s. 唔係 3xcoefficients on each side is equal...2A-6=-4 and -1=B2A = 4/6 and B=-1A = 1/3 and B = -1

words inside[this括號]is解釋,不用抄

1) 3(x-2)+2(A-2x)
=3x-6+2A-4x [1st step:evaluate until look like the other side]
=-x-6+2A

as -x-6+2A identity to Bx-4
so B=-X [2nd step:compare coefficient of like terms]
-6+2A=-4
A=1

2)(x+4)(2x-A)
=2x^2+8x-Ax-4A
=2x^2+(8-A)x-4A

as 2x^2+(8-A)x-4A identity to Bx^2 + 5x + C
so B=2
8-A=5
A=3
C=-4

3(x-2)+2(A-2x) ≡Bx-4
L.H.S:3x-6+2A-4x
=-x-6+2A
campare LHS and RHS
B=-1
-6+2A=-4
A=1

(x+4)(2x-A)≡Bx^2 + 5x + C
LHS:2x^2+8x-Ax-4A
=2x^2+x(8-A)-4A
campare LHS and RHS
B=2
8-A=5
A=3
-4A=C
C=-12