f.2數學..急~~(恆等式&聯立方程)20分!!!

1) 求下列中常數A及B的值
2(x^2-1)+Ax=(x+B)(2x-1)
L.H.S=2(x^2-1)+Ax
=2x^2-2+Ax
R.H.S=(x+B)(2x-1)
=2x^2-x+2xB-B
B=2
Ax=-x+2xB
Ax=-x+4x
A=x(4-1)/x
A=3


2) 解聯立方程(全部用代入消元法)
(x/4)+(y/3)=4
3y-2(x-1)=4

(x/4)+(y/3)=4
(3x/12)+(4y/12)=4
3x+4y=48
x=(48-4y)/3

代入第二條式:
3y-2(x-1)=4
3y-2{[(48-4y)/3]-1}=4
3y-{[(96-8y)/3]-2}=4
3y-(96-8y)/3=4-2
(9y-96+8y)/3=2
17y-96=6
17y=102
y=6
x=(48-4y)/3
=(48-24)/3
=8

3)
(x/2)+(y/3)=4
(x/4)+(y/2)=8

(x/2)+(y/3)=4
(3x+2y)/6=4
x=(24-2y)/3

代入第二條式:
(x/4)+(y/2)=8
{[(24-2y)/3]/4}+(y/2)=8
[(24-2y)/12]+(y/2)=8
(24-2y+6y)=96
4y=72
y=18
x=(24-2y)/3
=(-12)/3
=-4


4)
3a+3b-2=2a+2b-3
5a+b=2a+2b-3

3a+3b-2=2a+2b-3
3a-2a-2+3=2b-3b
a+1=-b
b=-1-a

代入第二條式:
5a+b=2a+2b-3
5a+(-1-a)=2a+2(-1-a)-3
5a-1-a=2a-2-2a-3
5a-a-2a+2a=1-2-3
4a=-4
a=-1
b=-1-a
=-1-(-1)
=0

5)
x-4=y/3
x+24=y

x-4=y/3
y=3x-12


代入第二條式:
x+24=y
x+24=3x-12
-2x=-36
x=18
y=3x-12
=54-12
=42

1. L.H.S.=2(x^2-1)+Ax
=2x^2-2+Ax
=2x^2+Ax-2
R.H.S.=(x+B)(2x-1)
=2x^2-x+2Bx-B
=2x^2+(2B-1)x-B
By comparing the coefficients on both sides, B=2, so A=2(2)-1=3.

2.(x/4)+(y/3)=4_____(1)
3y-2(x-1)=4_____(2)
(1)*12: 3x+4y=48
y=(48-3x)/4
Sub. this into (2)
3(48-3x)/4-2(x-1)=4
36-(9/4)x-2x+2=4
-(17/4)x=-34
(17/4)x=34
x=8
Sub x=8 into (2)
3y-2(8-1)=4
3y-14=4
3y=18
y=6
The solution is x=8 and y=6.

3. (x/2)+(y/3)=4_____(1)
(x/4)+(y/2)=8_____(2)
(1)*6: 3x+2y=24
y=(24-3x)/2
Sub this into (2)
(x/4)+(24-3x)/2/2=8
(x/4)+(24-3x)/4=8
(x+24-3x)/4=8
-2x+24=32
-2x=8
x=-4
Sub x=-4 into (2)
(-4/4)+(y/2)=8
-1+(y/2)=8
(y/2)=9
y=18
The solution is x=-4 and y=18.

4. 3a+3b-2=2a+2b-3
5a+b=2a+2b-3
Rearrange(1): a+b=-1_____(3)
Rearrange(2): 3a-b=-3
b=3a+3
Sub this in (3)
a+(3a+3)=-1
4a=-4
a=-1
Sub a=-1 into (3)
-1-b=-1
-b=0
b=0
The solution is a=-1 and b=0.

5. x-4=y/3_____(1)
x+24=y _____(2)
Put (2) into (1)
x-4=(x+24)/3
3(x-4)=x+24
3x-12=x+24
2x=36
x=18
Sub x=18 into (2)
18+24=y
y=42
The solution is x=18 and y=42.

1) 求下列中常數A及B的值
2(x^2-1) + Ax = (x+B)(2x-1)
x = 0, 2(-1) = (B)(-1)
B = 2
2(x^2-1) + Ax = (x+2)(2x-1)
x = 1, 2(1-1) + A = (1+2)(2-1)
A = 3
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2) 解聯立方程(全部用代入消元法)
(x/4)+(y/3)=4
3y-2(x-1)=4
(x/4) + (y/3) = 4
3x + 4y = 48
9x + 12y = 144 --------- (1)


3y-2(x-1)=4
2x - 3y = -2
8x - 12y = -8 --------- (2)
(1) + (2), 17x = 136, x = 8
3(8) + 4y = 48, y = 6
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3)
(x/2) + (y/3) = 4
3x + 2y = 24 --------- (1)

(x/4)+(y/2)=8
x + 2y = 32 ---------- (2)
(1) - (2), 同第二條一樣做
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4)
3a+3b-2=2a+2b-3
a + b = -1 --------- (1)

5a+b=2a+2b-3
3a - b = -3 ---------- (2)
(1) + (2), 同第二條一樣做
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5)
x-4=y/3
3x - 12 = y
3x - y = 12 --------- (1)

x+24=y
x - y = -24 ---------- (2)
(1) - (2), 同第二條一樣做
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2008-01-06 13:24:56 補充：
慢左, 不過記得支持我, 投我一票

1. 2(x2-1)+Ax=(x+B)(2x-1)
2x2+Ax-2=2x2-x+2Bx-B
2x2+Ax-2=2x2-x(1-2B)-B
∴B=2
A=-(1-2B)
A=2B-1
A=3
2. (x/4)+(y/3)=4-------------α
3y-2x=2---------------β
α x 9 - β
(9/4)x+2x=34
17x=136
x=8
∴y=(2+16)/3=6
3. (x/2)+(y/3)=4-------------α
(x/4)+(y/2)=8----------------β
α x 0.5-β
(1/6 - 1/2)y=-6
y=18
∴x=(8-9)4=-4
4. 3a+3b-2=2a+2b-3
a+b=-1-------------α
5a+b=2a+2b-3
3a-b=-3-------------β
α+β,
4a=-4
a=-1
∴b=-1-(-1)=0
5. x-4=y/3-------------α
x+24=y-----------β
α-β,
-28=(-2/3)y
y=42
∴x=42-24=18