✔ 最佳答案
圖片參考：
https://s.yimg.com/lo/api/res/1.2/ZQit8r6YM3UMER1bF6V.OQ--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/http://i.imgur.com/ZH9B85L.gif
哈哈哈，呢個《唔識做功課》系列係暑假都繼續：
「我連條題目都睇唔明!」
為左令你學習得更好，今次要詳盡ｄ講解一下！
1. A hall contains 216 seats. If the number of seats in each row is 6 more than the total number of rows of seats, how many rows of seats are there in the hall?
一個禮堂共有 216 個座位。若每一行的座位數比總行數多 6 ，問禮堂共有多少行座位。
Let n be the number of rows of seats in the hall.
Each row contains n + 6 seats.
n(n + 6) = 216
n² + 6n - 216 = 0
(n - 12)(n + 18) = 0
n = 12 or n = -18 (rejected)
Therefore, there are 12 rows of seats in the hall.
2. The Gateway Arch in the USA is 192 m tall. A ball initially at the rest is dropped from the top of the Gateway Arch. The distance (h m) that it falls t seconds is given by h = 5t². Find the time taken by the ball to reach the ground.
(give the answer correct to 2 decimal places.)
美國的聖路易斯拱門高 192 米。一個原本靜止的球從拱門頂掉下來。球在掉下 t 秒後所跌的距離是 h 米，其中 h = 5t²。問球到達地面的所需時間。（答案取至小數後兩個位。）
Consider h = 192.
h = 5t²
192 = 5t²
t² = 38.4
t = √38.4 or t = -√38.4 (rejected)
t = 6.196773354
The required time is 6.20 s (correct to 2 d.p.)
2014-08-13 19:36:18 補充：
3. A wire of length 20 cm is bent to form a rectangle. Can the area of the rectangle be 26 cm square?
一條長 20 cm 的電線屈曲成一個長方形，問這個長方形的面積能否是 26 cm²？
2014-08-13 19:37:23 補充：
Let the length of the rectangle be x cm.
The width is then (20/2 - x) = (10 - x) cm.
The area (in cm²) is
x(10 - x)
= 10x - x²
= -(x² - 10x)
= -(x² - 10x + 25 - 25)
= -(x² - 10x + 25) + 25
= -(x - 5)² + 25
≤ 25
The maximum area is 25 cm².
Thus, the area cannot be 26 cm².
2014-08-13 19:57:48 補充：
呢個係叫 completing the square (配方法)
即是弄一個完全平方 (perfect square) 出來。
善用 a² + 2ab + b² = (a + b)² 的道理。
當我們見到 x² + ax 的時候，可以故意這樣寫：
x² + ax + (a/2)² - (a/2)²
= x² + 2(a/2)x + (a/2)² - (a/2)²
= (x + a/2)² - (a/2)²
= (x + a/2)² - a²/4
明白嗎？
2014-08-13 20:13:54 補充：
╭∧---∧╮
│ .✪‿✪ │
╰/) ⋈ (\\╯
這個方法是用處是判斷二次函數 (quadratic function) 的最大 (maximum) 或最小 (minimum) 值，所以在數學上是有用的。
例如：
x² + 6x + 8
= (x + 2)(x + 4) 要懂得 factorize
= x² + 6x + 9 - 1
= (x + 3)² - 1 也要懂得 complete the square
≥ 0 - 1 = -1 即 minimum of x² + 6x + 8 is -1.
