Maths
回答 (5)
2009-12-31 3:08 am
✔ 最佳答案
If x + 1/x = 2, find the value of x^3 + 1/x^3x + 1/x = 2
x^2 + 1 = 2x
x^2 - 2x + 1 = 0
x = 1
x^3 + 1/x^3
= 1^3 + 1/(1)^3
= 1+1
= 2
2009-12-30 19:37:38 補充：
這不失為一個好方法~~~
對於這種比較簡單的題目，我認為還是直接點好~~
不過樓上亦展示另一種方法^^""[隨便一種都有分]]]
個人見議把題目改為"If x + 1/x = p+q, express the value of x^3 + 1/x^3 in terms of p and q." 會比較好~
2009-12-31 14:05:00 補充：
嗯~~~這題大概是打錯吧~~~要不然也不會這麼輕易解決~:P
參考: Hope can help you~~
2010-01-01 2:29 am
And also thanks for all guys' suggestions and solution.
2009-12-31 8:49 am
這不是中二的題目啊...
2009-12-31 4:16 am
ღ.｡.:* 知識就是力量╭★ 只有一時手快,如果出(x + 1/x) = p
(x + 1/x)^3 = x^3 + 3x + 3/x + 1/x^3 = p^3
x^3 + 1/x^3 = p^3 - 3p會有趣尐
(x + 1/x)^3 = x^3 + 3x + 3/x + 1/x^3 = p^3
x^3 + 1/x^3 = p^3 - 3p會有趣尐
2009-12-31 3:11 am
x+ 1/x =2
(x+1/x)^2=4
x^2+2+1/x^2=4
x^2+1/x^2=2
x^3+1/x^3
=(x+1/x)(x^2-1+1/x^2)
= 2 (2-1)
=2//
(x+1/x)^2=4
x^2+2+1/x^2=4
x^2+1/x^2=2
x^3+1/x^3
=(x+1/x)(x^2-1+1/x^2)
= 2 (2-1)
=2//
收錄日期: 2021-04-23 18:23:12
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20091230000051KK01633