MATHS F4 M2
2010-02-02 12:13 am
given that (1+2x)^n * (1-kx)^5=1-60x^2+terms involving higher
powers of x, where n is a positive integer. find the values of n and k.
回答 (1)
2010-02-02 3:37 am
✔ 最佳答案
(1+2x)^n * (1-kx)^5=[1+2nx+2n(n-1)x^2+...][1-5kx+10k^2x^2+...]
=1+(2n-5k)x+[2n(n-1)+10k^2-10nk]x^2
So 2n-5k=0 and 2n(n-1)+10k^2-10nk=-60
From the first equation, we have n=2.5k, substitute into the second equation
5k(2.5k-1)+10k^2-25k^2=-60
12.5k^2-5k-15k^2=-60
2.5k^2+50k-600=0
k^2+2k-24=0
(k+6)(k-4)=0
k=4 or k=-6 (rejected) and n=2.5k=10
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https://hk.answers.yahoo.com/question/index?qid=20100201000051KK00689