有關利用因式分解法解二次方程．．．好急呀！ ～

1). 7x (7x+1) + 1/4 = 0
49x^2 + 7x + 1/4 = 0 [a^2 + 2ab + b^2]--factorize it
(7x+1/2)^2 = 0
x = -1/14

2). 9x^2 = 1/7 (6x - 1/7)
9x^2 = 6x/7 - 1/49 [remove the denominator]
441x^2 = 42x - 1
441x^2 - 42x + 1=0 [a^2 - 2ab + b^2]--factorize it
(21x - 1)^2 = 0
x = 1/21

3). i don't know

4). 3x (4x - 1) = (2x + 1)^2
12x^2 - 3x = 4x^2 + 4x + 1
8x^2 - 7x - 1 = 0 [using factor method]
(8x + 1) (1x + 1) = 0
x = -1/8 or x = 1

5). (x+2) (3x - 2) = (x+6) (2x + 1)
3x^2 - 2x + 6x - 4 = 2x^2 + x + 12x +6
x^2 - 9x -10 = 0 [using factor method]
(x-10) (x+1) = 0
x = 10 or x = -1

6). (x-3)^2 = (1-4x)^2
x^2 - 6x + 9 = 1 - 8x + 16x^2
15x^2 -2x - 8 = 0 [using factor method]
(3x+2) (5x-4) = 0
x = -2/3 or x = 4/5

1. 7x(7x+1) +1/4 = 0
(7x)^2 + 2(1/2)(7x) + (1/2)^2 = 0
[7x + (1/2)]^2 = 0
7x+1/2 = 0
x = -1/14

2. 9x^2 = 1/7 (6x - 1/7 )
9x^2 - (6x/7) +(1/7)^2 = 0
(3x)^2 - 2(3x)(1/7) +(1/7)^2 = 0
(3x - 1/7)^2 = 0
3x-1/7 = 0
x = 1/21

2007-09-08 12:16:14 補充：
3. (3x 2) (3x 1) = 20 9x^2 9x 2 = 20 9x^2 9x - 18 = 0 x^2 x - 2 = 0 (x 2)(x-1) = 0 x = -2 OR x = 1

2007-09-08 12:16:57 補充：
4. 3x(4x - 1) = (2x 1)^2 12x^2 - 3x = 4x^2 4x 1 8x^2 - 7x - 1 = 0 (8x 1)(x-1) = 0 x = -1/8 OR x =1

2007-09-08 12:17:14 補充：
5. (x 2)(3x-2) = (x 6)(2x 1) 3x^2 4x - 4 = 2x^2 13x 6 x^2 - 9x - 10 = 0 (x-10)(x 1) = 0 x =10 OR x = -1

2007-09-08 12:17:32 補充：
6. 這題可以 a^2 - b^2 = (a b)(a - b) (x-3)^2 = (1-4x)^2 (x - 3)^2 - (1 - 4x)^2 = 0 [(x-3) (1 - 4x)] [(x-3) - (1 - 4x)] = 0 (-x - 2) ( 5x - 4) = 0 (x 2) (5x - 4) = 0 x = -2 OR x = 4/5

2007-09-08 12:18:14 補充：
P.S. 第1,2,6題都可以唔駛拆括號~~用我個方法會做得簡單d 舒服d希望幫到你啦~~~

2007-09-08 12:23:10 補充：
有d睇唔到加號= ="如果見到 x 2之類的..中間就係有個加號了..thanks

1.28x(7x+1)+1=0
196x^2+28x+1=0
(14x+1)^2=0
x=-1/14
2.63x^2=6x-1/7
441x^2-42x+1=0
(21x-1)^2=0
x=1/21
3.9x^2+9x-18=0
x^2+x-2=0
(x+2)(x-1)=0
x=-2 OR 1
4.12x^2-3x=4x^2+4x+1
8x^2-7x-1=0
(8x+1)(x-1)=0
x=-1/8 OR 1
5.3x^2+4x-4=2x^2+13x+6
x^2-9x-10=0
(x-10)(x+1)=0
x=10 OR -1
6.x^2-6x+9=1-8x+16x^2
15x^2-14x-8=0
(3x-4)(5x+2)=0
x=4/3 OR -2/5