新加坡A level考题，STPM的可以进来试试看 [开始不断更新]

無聊人

tayks88，我在新加坡就读
什么Mathematics S/T我不知道

dunwan2tellu

further math 1)

Let x^3 - px^2 + qx - r = 0 has the root a,b,c . Then

p = a+b+c=0
q = ab+bc+ca = 1/2 [ (a+b+c)^2 - (a^2+b^2+c^2)] = -8
Denote Sk as the sum of degree k , then by Newton Sum ,
S3 - pS2 + qS1 - 3r = 0 ==> -9 - 3r = 0 --> r = -3

==> x^3 - 8x - 3 = 0
==> x^4 - 8x^2 - 3x = 0
Again by Newton Sum S4 - 8S2 - 3S1 = 0 --> S4 = 8(16) = 128

**Note : Sk = a^k + b^k + c^k

dunwan2tellu

無聊人

原帖由 dunwan2tellu 于 19-5-2006 12:55 PM 发表

第8题错了

dunwan2tellu

type 错了。应该是 Sqrt{1-k}=2i ==> k = 5 之后求得 A = 1/8

所以 y = e^(-x){cos2x +sqrt{3}sin2x} + 1/8 e^x