唔識計呀 , 請幫忙
1. If y = (2 x + 3)^n , where n is an integer , satisfies the equation
(2x + 3)^2 (d^2 y / dx^2) - 9(2x +3) (dy / dx) + 10y = 0
find the value of n.
F.4 AMaths
2007-06-07 5:56 am
回答 (2)
2007-06-07 6:11 am
✔ 最佳答案
dy / dx = 2n (2 x + 3)^(n-1)d^2 y / dx^2 = 4n(n-1) (2 x + 3)^(n-2)
(2x + 3)^2 4n(n-1) (2 x + 3)^(n-2) - 9(2x +3) 2n (2 x + 3)^(n-1) + 10(2 x + 3)^n = 0
[ 4n(n-1) - 18n + 10 ](2 x + 3)^n = 0
4n(n-1) - 18n + 10 = 0
2n^2 - 11n + 5 = 0
(2n-1)(n-5) = 0
n = 5 or n = 1/2 (rejected)
2007-06-07 5:58 am
This is so easy for me!
n=56
n=56
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070606000051KK04654