唔識做功課26

圖片參考：https://s.yimg.com/lo/api/res/1.2/ZQit8r6YM3UMER1bF6V.OQ--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/http://i.imgur.com/ZH9B85L.gif

Let x cm be the side of the isosceles right-angled triangle.

Then, by Pythagoras theorem, the hypotenuse is
√(x² + x²) = √(2x²) = √2 x cm

Therefore, the perimeter of the triangle is
x + x + √2 x
= (1 + 1 + √2)x
= (2 + √2)x (cm)

Consider (2 + √2)x = 4
x = 4/(2 + √2)
x = 4/(2 + √2) × (2 - √2)/(2 - √2)
x = 4(2 - √2)/(4 - 2)
x = 4(2 - √2)/2
x = 2(2 - √2)
x = 4 - 2√2

The length of the hypotenuse of the triangle is
√2 x
= √2 (4 - 2√2)
= (4√2 - 4) cm



圖片參考：https://s.yimg.com/rk/HA00430218/o/1610793754.jpg


2014-09-14 17:42:17 補充：
這樣看吧：

　√(2x²)
= √2√(x²)
= √2 x

2014-09-14 19:02:10 補充：
補充發問：
why!!!!!! × (2 - √2)/(2 - √2)

補充回答：
由於你見到分母有 (2 + √2) 這個項目。
我們為了方便計算，要做一個叫 rationalization of denomination （分母有理化）的步驟。
因此，要分子分母都乘 (2 - √2)，再計算。

至於為什麼要乘 (2 - √2) 呢？
那是因為你見到有 (2 + √2)，那麼如果你乘了 (2 - √2) 就可得 4 - 2 = 2，沒有根號 (surd) 了。

背後用的原理是： (a + b)(a - b) ≡ a² - b²

2014-09-14 19:04:47 補充：
問：
A rectangular garden is 10 m wide and 30 m long. It is surrounded by a path of uniform width. If the area of the path is 176 m², find the width of the path.

答：
Let the width be x m.
(30 + 2x)(10 + 2x) - (30)(10) = 176
2(15 + x)2(5 + x) - 300 = 176
4(15 + x)(5 + x) = 476

2014-09-14 19:05:30 補充：
(15 + x)(5 + x) = 119
x² + 20x + 75 = 119
x² + 20x - 44 = 0
(x + 22)(x - 2) = 0
x = 2 or x = -22 (rejected)

The width is 2 m.

2014-09-14 19:21:21 補充：
問：
Sharon's deposit Question

答：
500000 × (1 + r%) × [1 + (r + 1)%] = 500000 + 25300
(1 + r/100) × [1 + (r + 1)/100] = 1.0506
(100 + r) × [100 + (r + 1)] = 10506
(100 + r)(101 + r) = 10506
10100 + 201r + r² = 10506
r² + 201r - 406 = 0
(r + 203)(r - 2) = 0
r = 2 or r = -203 (rejected)

ASK YOUR TEACHER!!!!!!!!!!

√(2x²) = √2 x
Help...I don't know why


因為二次方只屬於x而不屬於2

若果平方共同擁有

那該是

√(2x)²


此外, x的平方再加平方根是變為x

由於2沒有平方

所以它依舊也擁有平方根