一元二次方程F.4

全部都是拆開括號，將所有項搬去一邊，轉換成
ax²＋bx＋c＝0
然後套用公式就成了。試試！

2015-01-27 21:04:00 補充：
公式係：x＝[-b＋√(b²－4ac)]/(2a) 或 x＝[-b－√(b²－4ac)]/(2a)

33.
(x + 3)(2x + 1) + 3 = 0
2x² + x + 6x + 3 + 3 = 0
2x² + 7x + 6 = 0
x = [-7＋√(49－4*2*6)]/4 或 [-7－√(49－4*2*6)]/4
所以，x＝-3/2 或 x = -2

2015-01-29 10:42:51 補充：
38.) 　
[(3x-3) + (7-x)][(3x-3) - (7-x)] = 0
[(3x-x-3+7)] [(3x+x-3-7)] = 0 ⋯⋯ (漏了＝0, 之後全部都漏了)
(2x+4) (4x-10) = 0
2(x+2) 2(2x-5) = 0
(x+2) (2x-5) = 0 ⋯⋯⋯⋯⋯⋯⋯ (兩邊除以4)
x+2 = 0 or 2x-5 = 0
x = -2 or 5/2

2015-02-04 08:57:12 補充：
5x(x - 2) = (x - 2)^2
5x(x - 2) - (x - 2)^2 = 0
(x - 2)(5x - x + 2) = 0 .... (抽因子)
(x - 2)(4x + 2) = 0
x - 2 = 0 或 4x + 2 = 0
x = 2 或 x = -1/2

33.
2x² + 7x + 6 = 0
(2x + 3)(x + 2) = 0 (2x + 3)(x + 2)怎樣得出2x² + 7x + 6??

由2x² + 7x + 6 = 0

37.

[(x - 2) + (4 - 5x)][(x - 2) - (4 - 5x)] = 0
(-4x + 2)(6x - 6) = 0
(2x - 1)(x - 1) = 0這個也一樣

2015-01-27 16:28:36 補充：
38.) 9(x-1)^2 = (7-)^2

括號外的9 怎樣處理?? 乘x和1嗎?
9(x-1)^2 - (7-)^2 =0

[ 9 (x - 1 ) + (7 - x) ] [9 (x - 1) - (7 - x) ] = 0

[ (9x - 9 ) + (7 - x) ] [ (9x - 9) - (7 + x) ] = 0

2015-01-28 10:56:53 補充：
-2(2x - 1) 並 (6x - 6) = 6(x - 1)都除 -12 ??
等於(2x - 1)(x - 1) = 0
x = 1/2 or x = 1 ?

38.) 　
[(3x - 3) + (7 - x)][(3x - 3) - (7 - x)] = 0
[(3x - x-3+7)] [(3x+x-3-7)]

(2x+4) (4x-10)
2(x+2) 2(2x-5)
(2x+1) (2x-5)
(2x+1) (2x-5)
2x+1 or 2x-5 =0
之後是這樣??但答案是-2, - 5/2

2015-02-03 21:46:39 補充：
5x(x-2)=(x-2)^2


5的話又怎樣做?5這個數字沒辦法做平方

圖中有十七條問題。。。

2015-01-27 14:09:25 補充：
講解少少，你先自己試做，對書後的答案，真的仍不懂才再問。
因為不可能這樣子幫你做十七題數的。

23.
x² = 5x - 25/4
全式乘４可得
4x² = 20x - 25
4x² - 20x + 25 = 0
(2x - 5)² = 0
x = 5/2 (重根)

2015-01-27 14:10:27 補充：
33.
(x + 3)(2x + 1) + 3 = 0
2x² + 7x + 3 + 3 = 0
2x² + 7x + 6 = 0
(2x + 3)(x + 2) = 0
x = -3/2 or x = -2

2015-01-27 14:11:42 補充：
37.
(x - 2)² = (4 - 5x)²
(x - 2)² - (4 - 5x)² = 0
[(x - 2) + (4 - 5x)][(x - 2) - (4 - 5x)] = 0
(-4x + 2)(6x - 6) = 0
(2x - 1)(x - 1) = 0
x = 1/2 or x = 1

2015-01-27 14:14:20 補充：
39.

24 = 1 × 24
24 = 2 × 12
24 = 3 × 8
24 = 4 × 6
24 = -1 × (-24)
24 = -2 × (-12)
24 = -3 × (-8)
24 = -4 × (-6)
把 x² + kx + 24 = 0 的左方作因式分解可以是：
(x - 1)(x - 24)
(x + 1)(x + 24)
(x - 2)(x - 12)
...等等

2015-01-27 14:14:52 補充：
故 k 的可能值包括：
1 + 24 = 25
-1 + (-24) = -25
2 + 12 = 14
-2 + (-12) = -14
3 + 8 = 11
-3 + (-8) = -11
4 + 6 = 10
-4 + (-6) = -10

共八個。

2015-01-27 23:43:33 補充：
先回意見007：

33.
由 2x² + 7x + 6 變 (2x + 3)(x + 2) 是因式分解，是中三的課題。
由 (2x + 3)(x + 2) 變 2x² + 7x + 6 是擴展數式，是中一的課題。

37.
(-4x + 2) = -2(2x - 1) 並 (6x - 6) = 6(x - 1)
全式左右都除 -12 即可

2015-01-27 23:45:31 補充：
再回意見008：

應考慮因式分解，你要對於平方數比較敏感，這樣計數才會快。

9(x - 1)² = (7 - x)²
3²(x - 1)² = (7 - x)²
[3(x - 1)]² = (7 - x)²
(3x - 3)² = (7 - x)²
(3x - 3)² - (7 - x)² = 0
[(3x - 3) + (7 - x)][(3x - 3) - (7 - x)] = 0
．．．