F.4 maths rational functions
2010-01-15 1:58 am
if x-1/x=a,express x^3-1/x^3 in terms of a .Give your answer in the simplest form
回答 (3)
2010-01-15 2:07 am
✔ 最佳答案
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2010-01-14 18:57:21 補充：
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2010-01-15 2:48 am
這條問題跟我早前發問的問題很相似~
有善心既網友都發表左相近既意見
詳見:
http://hk.knowledge.yahoo.com/question/question?qid=7009123001633
有善心既網友都發表左相近既意見
詳見:
http://hk.knowledge.yahoo.com/question/question?qid=7009123001633
2010-01-15 2:08 am
x - 1/x = a
(x - 1/x)^3 = a^3
(x^2 - 2 + 1/x^2)(x - 1/x) = a^3
x^3 - 3x + 3/x - 1/x^3 = a^3
x^3 - 1/x^3 = a^3 + 3(x - 1/x)
x^3 - 1/x^3 = a^3 + 3a
(x - 1/x)^3 = a^3
(x^2 - 2 + 1/x^2)(x - 1/x) = a^3
x^3 - 3x + 3/x - 1/x^3 = a^3
x^3 - 1/x^3 = a^3 + 3(x - 1/x)
x^3 - 1/x^3 = a^3 + 3a
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原文連結 [永久失效]:
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