1/x = x^ -1 -------why?
謝
更新1:
點解 1/x = 1 * x^ -1
1/x = x^-1
回答 (3)
2011-05-13 5:15 pm
✔ 最佳答案
x ^0 =1 -------------why?1/x=x^(－1)-------why?
Sol
x ^0 =1 -------------why?
x^0=1 在大部份情況為真，但終究為錯誤命題
修正如下
當x<>0時 x^0=1
證明
x<>0
x/x=1
x^1/x^1=1
x^(1－1)=1
x^0=1
1/x=x^(－1)-------why?
同上為錯誤命題
修正如下
當x<>0時 1/x=x^(－1)
證明
x<>0
1/x=x^0/x^1=x^(0－1)=x^(－1)
2011-05-13 3:30 pm
(1) By index law, a^m / a^n = a^(m - n).
Put m =n
LHS : a^m /a^n = a^m / a^m = 1.
RHS: a^(m - m) = a^0
so a^0 = 1.
(2) Put m = 0 , n = 1
LHS : a^0 / a^1 = 1/a (using above result)
RHS : a^(0 - 1) = a^(-1)
so 1/a = a^(- 1).
Put m =n
LHS : a^m /a^n = a^m / a^m = 1.
RHS: a^(m - m) = a^0
so a^0 = 1.
(2) Put m = 0 , n = 1
LHS : a^0 / a^1 = 1/a (using above result)
RHS : a^(0 - 1) = a^(-1)
so 1/a = a^(- 1).
2011-05-13 11:34 am
x^0 = x^(1 - 1) = x^1 / x^1 = 1
1/x = 1 * x^ -1 = x^ -1
1/x = 1 * x^ -1 = x^ -1
收錄日期: 2021-04-21 22:27:42
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