1)Find the coefficient of x^-12 in the expansion of [x^3-(1/x)]^24.
2a)If a and b are the roots of the equation x^2+px+q=0, express a^3+b^3 and (a-b^2)(b-a^2) in terms of p an q.
2b)Deduce that the condition for one root of the equation to be the square of the other is p^3-3pq+q^2+q=0.
中4附加數
2008-01-10 4:42 am
回答 (1)
2008-01-10 6:27 am
✔ 最佳答案
1. constant term: 24Cr (x^3)^(24-r) (-1/x)^r =24Cr (x^(72-4r))(-1)^rtherefore the coefficient is:24C21 (x^(72-4(21)))(-1)^21
= -2024x^-12
2a. a+b= -p
ab=q
a^3+b^3
= (a+b)^3-3a^2b -3ab^2
= (a+b)^3-3ab(a+b)
= -p^3+3pq
(a-b^2)(b-a^2)
= ab-a^2b^2-(a^3+b^3)
= q+q^2+p^3-3pq
收錄日期: 2021-04-28 13:47:37
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