推 Philethan : 感謝！那兩小時確實讓我對許多人的解法印象深刻XD 06/20 18:05
※ 引述《Philethan (PE)》之銘言：
: 例一：
: 在 Chapter 11: Infinite Sequences and Series，Problem Plus 第25題
: u = 1 + x^3/3! + x^6/6! + x^9/9!
: v = x + x^4/4! + x^7/7! + x^10/10!
: w = x^2/2! + x^5/5! + x^8/8! + x^11/11!
: 證明 u^3 + v^3 + w^3 - 3uvw = 1
: 我怎麼想都想不出來....超級痛苦，已經想2小時了。
: 我觀察到
: u'=w, w'=v, v'=u u+v+w = exp(x)
: 那又怎樣呢！有想過 (u+v+w)^3 = ????，但總覺得這好像很複雜，應該不太可能。
(u^3 + v^3 + w^3 - 3uvw)' = 3u^2 u' + 3v^2 v' + 3w^2 w' - 3 u'vw - ...
and since u'=w, w'=v, v'=u ..., ...
It definitly worth your time, two hours or more
Try to have fun and play with it, even you didn't solve this problem,
you still got something.
The answers given by me and others are worthless to you
without that two hours of exploring.
--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 180.176.36.13
※ 文章網址: https://www.ptt.cc/bbs/Math/M.1434793599.A.9ED.html
※ 編輯: weijr (180.176.36.13), 06/20/2015 17:51:05