(a)
Given that n is a positive integer, expand (1-px)^6 - (1+x)^n in ascending powers of x up to the term in x^2.
(b)
If the coefficients of x and x^2 in the expansion are -17 and 50 respectively, find the values of n and p.
binomial theorem-4-
2009-10-26 11:22 pm
回答 (1)
2009-10-27 2:29 am
✔ 最佳答案
(a) (1 - px)6 = 1 - 6px + 15p2x2 + ...(1 + x)n = 1 + nx + n(n - 1)x2/2 + ...
(1 - px)6 - (1 + x)n = - (6p + n)x + [15p2 - n(n - 1)/2]x2 + ...
(b) With:
- (6p + n) = - 17
6p + n = 17 ... (1)
15p2 - n(n - 1)/2 = 50
30p2 - n2 + n = 100
30p2 - (17 - 6p)2 + 17 - 6p = 100
30p2 - 289 + 204p - 36p2 - 83 - 6p = 0
- 6p2 + 198p - 372 = 0
p2 - 33p + 62 = 0
(p - 31)(p - 2) = 0
p = 31 or p = 2
n = - 169 (rejected) or 5
So p = 2 and n = 5
參考: Myself
收錄日期: 2021-04-13 16:54:16
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20091026000051KK01139