(1+ax+bx^2)^n = 1+ nax + (nb+nC2 a^2) x^2 + (2 nC2 ab+nC3 a^3) x^3+......
If (1+ax+bx^2)^n =1+7x-7x^2+ terms involving higher powers of x, where a and b are integers, find the values of a,b and n.
a.math ( binomial theorem)
2006-10-15 2:59 am
回答 (1)
2006-10-15 5:39 am
✔ 最佳答案
We have7 = an......................(1)
nb + nC2 a^2 = -7....(2)
As a and n are integers, we have n = 7.
[n cannot be 1 as we have the term x^3. Also n cannot be negative.]
Thus a = 1.
Sub n = 7 and a = 1 in (2),
7b + 7C2 (1)^2 = -7
7b + 21 = -7
7b = -28
b = -4
收錄日期: 2021-04-13 13:44:18
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20061014000051KK04593