急!幾條中2easy問題!!

您好，我是 lop****** ，高興能解答您的問題。

1a)

(3y-A)y+1≡3y^2+2y+B
3y^2 - Ay + 1 ≡ 3y^2 + 2y + B
A = -2 , B = 1

1b)

x(x-B)≡x^2+x+A
x^2 - Bx ≡ x^2 + x + A
x^2 - Bx + 0 ≡ x^2 + 1x + A
A = 0 , B = -1

1c)

If (x+2)(Cx+B)≡3x^2+4x+A,where A,B and C are constants, find A,B and C

(x+2)(Cx+B)≡3x^2+4x+A
x(Cx+B) + 2(Cx+B) ≡ 3x^2 + 4x + A
Cx^2 + Bx + 2Cx + 2B ≡ 3x^2 + 4x + A
Cx^2 + (B+2C)x + 2B ≡ 3x^2 + 4x + A

C = 3 --- (1)
B+2C = 4 --- (2)
2B = A --- (3)

From (1) ,

B+2C = 4
B + 2×3 = 4
B + 6 = 4
B = -2 --- (4)
Sub (4) into (3)

2×-2 = A
A = -4

Answer : A = -4 , B = -2 , C = 3 .

1d)

If A(2x+1)^2-3Bx+(B-C)≡(4x-1)(x-4), where A,B and C are constants, find A,B and C

A(2x+1)^2-3Bx+(B-C)≡(4x-1)(x-4)
A[2x(2x+1)+1(2x+1)] - 3Bx + B - C ≡ 4x(x-4) - 1(x-4)
A(4x^2+2x+2x+1) - 3Bx + B - C ≡ 4x^2 - 16x - x + 4
4Ax^2 + 4Ax + A - 3Bx + B - C ≡ 4x^2 - 17x + 4
(4A)x^2 + (4A-3B)x + (A+B-C) ≡ 4x^2 - 17x + 4

4A = 4 --- (1)
4A - 3B = -17 --- (2)
A+B-C = 4 --- (3)

From (1) :
A = 1 --- (4)

Sub (1) into (2) ,
4 - 3B = -17
3B = 21
B = 7 --- (5)

Sub (4) and (5) into (3) ,

1 + 7 - C = 4
C = 4

Answer : A = 1 , B = 7 , C = 4 .

----------------------------------------------------------
2a)

3y+5/2-816y/5=9(3y+1)/10
10(3y+5/2-816y/5) = 10[9(3y+1)/10]
30y + 25 - 1632y = 9(3y+1)
25-1602y = 27y + 9
16 = 1629y
y = 16/1629

2b)

3(2x-1)^2+6x^2=2(3x-1)^2+1
3(4x^2-4x+1) + 6x^2 = 2(9x^2-6x+1) + 1
12x^2 - 12x + 3 + 6x^2 = 18x^2 - 12x + 2 + 1
18x^2 - 12x + 3 = 18x^2 - 12x + 3
Ture
----------------------------------------------------------
3)

(y+1)(y-2)=(y-1)^2+y-3
y^2 - y - 2 = y^2 - 2y + 1 + y - 3
y^2 - y - 2 = y^2 - y - 2
Ture

----------------------------------------------------------

4a)

(3x+5y)(10y-6x)
= 2[(3x+5y)^2]
= 2(9x^2+30xy+25y^2)
= 18x^2 + 60xy + 50y^2

4b)

a(2a+b/3)(2a-b/3)
= a[(2a)^2-(b/3)^2]
= a(4a^2-b^2/9)
= 4a^3 - ab^2/9

5a)

(2a+b)^2-(a+2b)^2=3(a+b)(a-b)
4a^2+4ab+b^2 - (a^2+4ab+4b^2) = 3(a^2-b^2)
3a^2 - 3b^2 = 3a^2 - 3b^2
Ture

5b)

Hence,evaluate 20001^2-10002^2

Let a = 10000 , b = 1

20001^2-10002^2
= (2a+b)^2 - (2b+a)^2
= 3(a-b)(a+b)
= 3a^2 - 3b^2
= 300000000 - 3
= 299999997

2011-09-01 16:52:03 補充：
But I think 2a) has a typing mistake or he missed a pair of brackets .

2a) 3y+5/2-816y/5=9(3y+1)/10

816y = ="

TsuiHiulam used the blankets and the '^' and the '/' very well!
very clear!

2011-09-01 19:19:57 補充：
??.............