國二數學-配方法與公式解

2121212135

2014-01-01 23:03:33 補充：
https://www.flickr.com/photos/113125345@N06/11687256873/

2014-01-01 23:12:42 補充：
第四題答案被切到，m就是被切到左邊的那個m值:正負根號五

2014-01-02 13:21:57 補充：
第三提正負號搞錯@@

b^2-4ac=(4)^2-4*(5/2)*c=31

c=-(3/2)

最後結果為m=-3

2014-01-16 22:02:22 補充：
好吧，我承認是為了要2500點以上的特殊功能，所以這麼做，既然造成反感，以後不會這樣了，我會公平競爭

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1.
2(x - 7)² + 4 = 0
(x - 7)² + 2 = 0
(x - 7)² = 2
x - 7 = ±(√2)i .. where i = √-1
x = 7 + (√2)i 或 x = 7 + (√2)i


2.
(3x)² + 4x + 1 = 0
(3x)² + 2(3x)(2/3) + 1 = 0
[(3x)² + 2(3x)(2/3) + (2/3)²] - (2/3)² + 1 = 0
[3x + (2/3)]² = -5/9
3x + (2/3) = ±(√5)i/3
3x = [-2 ± (√5)i]/3
x = [-2 + (√5)i]/9 或 x = [-2 + (√5)i]/9


3.
5x² + 8x + m = 0
5[x² + (8/5)x] + m = 0
5[x² + (8/5)x + (4/5)²] - 5(4/5)² + m = 0
5[x + (4/5)]² = (16 - 5m)/5
[x + (4/5)]² = (16 - 5m)/25
x + (4/5) = ±[√(16 - 5m)]/5 ...... [1]

已知：x + (4/5) = ±(√31)/5 ......[2]

[1] = [2] :
[√(16 - 5m)]/5 = (√31)/5
16 - 5m = 31
5m = -15
m = -3


4.
設x² + (m² - 5)x - 6 = 0 的兩根為 u 及 -u。

x = u 或 x = -u
(x - u) = 0 或 (x + u) = 0
(x - u)(x + u) = 0
x² - u² = 0

比較兩方程的 x 項：
m² - 5 = 0
m² = 5
m = √5 或 m = -√5

另解：
設x² + (m² - 5)x - 6 = 0 的兩根為 u 及 -u。

兩根之和：
-(m² - 5) = u + (-u)
m² - 5 = 0
m² = 5
m = √5 或 m = -√5


5.
4(x + 5²) = 7
4(x + 25) = 7
x + 25 = 7/4
x + (100/4) = 7/4
x = -93/4

若題目為 4(x + 5)² = 7 之誤，則：
4(x + 5)² = 7
(x + 5)² = 7/4
x + 5 = ±(√7)/2
x + (10/2) = ±(√7)/2
x = (-10 + √7)/2 或x = (-10 - √7)/2