a.設x+1/x=a 。試以 a表示x^2+1/x^2 。
b.由此，解方程
6(x^2+1/x^2)-5x(x+1/x)-38=0
步驟要詳細一點 唔該晒!
中４ 數學一條
2007-10-14 6:51 pm
回答 (1)
2007-10-14 7:23 pm
✔ 最佳答案
a. x + 1/x = a (x + 1/x)2 = a2
x2 + 2 + 1/x2 = a2
x2 + 1/x2 = a2 – 2
b. 6(x2 + 1/x2) + 5(x + 1/x) – 38 = 0
6(a2 - 2) + 5a – 38 = 0
6a2 + 5a – 50 = 0
(2a - 5)(3a + 10) = 0
a = 5/2 or -10/3
So, when a = 5/2
x + 1/x = 5/2
2x2 – 5x + 2 = 0
(2x - 1)(x - 2) = 0
x = 1/2 or 2
When a = -10/3
x + 1/x = -10/3
3x2 + 10x + 3 = 0
(3x + 1)(x + 3) = 0
x = -1/3 or -3
參考: Myself~~~
收錄日期: 2021-04-26 13:29:10
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