求未知數為次方

One is simple, one is not so simple

圖片參考：https://s.yimg.com/lo/api/res/1.2/sMN3r.vjdadjR5IK8SKheA--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/http://i187.photobucket.com/albums/x22/cshung/7015033100112-2_zpsoje9ba9x.png


2015-04-01 03:47:10 補充：
Thanks - yeah - same idea applies with this variation too, even simpler as follow:

12.5 = (y-1)/0.07y
0.875y = y - 1

0.125y = 1
y = 8

n = log 8 / log 1.07

2015-04-02 03:54:25 補充：
5次方polynomial係唔可能有辦法用root extraction operators搵x，這是Galois Theory，已經證明左係唔可能。

只能用numerical methods，而bisection method係我識既numerical method中最簡單的。

2015-04-02 04:35:44 補充：
Perhaps unrelated - reflecting on myself, I don't really know how to find complex root for the polynomial. Bisection obviously won't cut it, so I searched.

Here you go, Bairstow's method can find you a pair of root at the same time.

Q1 thank you

But Q2 有無簡單d 方法

8 = [(1+x)^5) -1] ÷ x

太長唔識計

我睇你呢兩題的樣，你似係學緊 annuity。

由於無 closed-form, solve yield rate 的方法有以下：
＊電腦 Excel, Wolfram Alpha
＊查 Interest table
＊用 numerical method 如 bisection, Newton's method

2015-04-01 00:10:21 補充：
當然，用 financial calculator 都是一個好方法。
（如果你真的在學 financial mathematics。）

2015-04-01 02:45:03 補充：
我懷疑第一題其實是

　12.5 = (1.07ⁿ - 1) / [0.07(1.07)ⁿ]

因為這即是

　12.5 = (1 - 1.07⁻ⁿ) / 0.07

這是 present value of annuity-immediate。

不過這因為只是 solve for time period (n)，不是 yield rate，所以可以計到。

2015-04-02 00:35:57 補充：
你這個好明顯真的是 annuity 的計算。

如果你是可以用 financial calculator 的話, 你應該用以計算。

如果你一定要用 scientific calculator 的話, 你則要用 numerical method。