設a 是有理數 ,(5-a「2)/(2+4「2) 也是有理數 ,則a之值為
(「 是開方)
maths求救
2011-03-02 3:21 am
回答 (2)
2011-03-02 3:33 am
✔ 最佳答案
設(5 - a√2) / (2 + 4√2) = k , (a 和 k 是有理數)5 - a√2 = 2k + 4k√25 - 2k = (a + 4k) √2有理數 = 有理數 * 無理數√2a + 4k 必為 0 ,從而 5 - 2k = 0k = 2.5
代入
a + 4k = 0a + 4*2.5 = 0a = - 10
2011-03-02 3:41 am
另一做法：
(5 - a√2) / (2 + 4√2)
= (5 - a√2)(1 - 2√2) / 2(1 + 2√2)(1 - 2√2)
= (5 - a√2 - 10√2 + 4a) / 2[1² - (2√2)²]
= [(5 + 4a) - (a + 10)√2] / (-14)
若上式為有理數，則
(a + 10)√2 = 0
a + 10 = 0
a = -10 ...... (答案)
(5 - a√2) / (2 + 4√2)
= (5 - a√2)(1 - 2√2) / 2(1 + 2√2)(1 - 2√2)
= (5 - a√2 - 10√2 + 4a) / 2[1² - (2√2)²]
= [(5 + 4a) - (a + 10)√2] / (-14)
若上式為有理數，則
(a + 10)√2 = 0
a + 10 = 0
a = -10 ...... (答案)
收錄日期: 2021-04-21 22:18:44
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https://hk.answers.yahoo.com/question/index?qid=20110301000051KK00860