已知 x+1/x=3. (a)找出 x^2+1/x^2. (b)使用結果在題a,找出x^3+1/x^3

a) (x+1/x)^2=9
x^2+2x(1/x)+1/x^2=9
x^2+1/x^2=7

b)
x^3+1/x^3=(x+1/x)[x^2-x(1/x)+1/x^2]
=3(7-1)
=18

2007-02-17 18:51:32 補充：
identity:(a+b)^2=a^2+2ab+b^2a^3+b^3=(a+b)(a^2-ab+b^2)

http://x22.xanga.com/2d0d0bf007531107263201/t75980779.gif
你上去睇睇

2007-02-17 21:06:28 補充：
http://x05.xanga.com/b8dd5af0c4c32107263667/t75981166.gifhttp://x05.xanga.com/b8dd5af0c4c32107263667/t75981166.gifhttp://x05.xanga.com/b8dd5af0c4c32107263667/t75981166.gif呢個先岩

2007-02-17 21:10:19 補充：
http://x7f.xanga.com/69dd376142c30107264114/t75981565.gifhttp://x7f.xanga.com/69dd376142c30107264114/t75981565.gifTHIS IS CORRECTSORRY~

(a)
(x+1/x)^2 = x^2 + 2(x)(1/x) + (1/x)^2
(3)^2 = x^2 + 2 + 1/x^2
9 = x^2 + 1/x^2 +2
--> x^2 + 1/x^2 = 9-2 = 7


(b)
(x + 1/x)^3 = x^3 + 3(x^2)(1/x) + 3(x)(1/x^2) + (1/x)^3
(3)^3 = x^3 + 3x + 3(1/x) + 1/x^3
27 = x^3 + 1/x^3 + 3(x + 1/x)
= x^3 + 1/x^3 + 3(3)
= x^3 + 1/x^3 + 9
--> x^3 + 1/x^3 = 27-9 = 18