It is given that x + 1/x = 3
a) Find the value of (x^2) + 1/(x^2).
b)Using the result in a), find the value of (x^3) + 1/(x^3)
S.2 Maths
2007-03-31 4:13 am
回答 (2)
2007-03-31 4:42 am
✔ 最佳答案
a) x + 1/x = 3( x + 1/x)^2 = 3^2(兩邊一讀square)
x^2 +2+1/(x^2)=9
(x^2) + 1/(x^2)=7
b)(x^3) + 1/(x^3)
=(x + 1/x)(x^2-1+1/x^2) (抽個(x + 1/x)出黎)
=3(7-1)
=18
2007-03-30 20:43:08 補充：
sor,,,打錯個齊字做讀字
參考: 自己
2007-03-31 4:34 am
(a)
x + 1/x = 3
(x + 1/x)^2 = 3^2
x^2 + 2(x)(1/x) + (1/x)^2 = 9
x^2 + 2 + 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)
= 24
x + 1/x = 3
(x + 1/x)^2 = 3^2
x^2 + 2(x)(1/x) + (1/x)^2 = 9
x^2 + 2 + 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)
= 24
收錄日期: 2021-04-12 18:50:18
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070330000051KK03437