請問x^x=x，x值為多少?
回答 (6)
2019-08-13 1:04 am
x^x = x
兩邊開x次方得 x = x^(1/x)
於是 x^x = x^(1/x)
x = 1/x
x² = 1
x = ±1
兩邊開x次方得 x = x^(1/x)
於是 x^x = x^(1/x)
x = 1/x
x² = 1
x = ±1
2019-08-11 7:46 pm
請問x^x=x，x值為多少?
Sol
(1)
x>0
x^x=x
ln(x^x)=lnx
xlnx=lnx
xlnx－lnx=0
(x－1)lnx=0
X－1=0 or lnx=0
x=1 or x=1
x=1……………………………..
(2) x<0
x^x=x
Set y=－x
y>0
(－y)^(－y)=－y
y^(－y)=y
ln[y^(－y)]=lny
(－y)lny=lny
－ylny-lny=0
(－y－1)lny=0
－y－1=0 or lny=0
y=－1(不合) or y=1
x=－1……………………………
Sol
(1)
x>0
x^x=x
ln(x^x)=lnx
xlnx=lnx
xlnx－lnx=0
(x－1)lnx=0
X－1=0 or lnx=0
x=1 or x=1
x=1……………………………..
(2) x<0
x^x=x
Set y=－x
y>0
(－y)^(－y)=－y
y^(－y)=y
ln[y^(－y)]=lny
(－y)lny=lny
－ylny-lny=0
(－y－1)lny=0
－y－1=0 or lny=0
y=－1(不合) or y=1
x=－1……………………………
2019-08-24 3:35 pm
在C++程式語法中
^ 為 XOR
XOR有一種特性叫互斥
也就是說兩個一樣的數做XOR必為0
也就是說
x^x=0
那
x=0就是唯一的解啦
^ 為 XOR
XOR有一種特性叫互斥
也就是說兩個一樣的數做XOR必為0
也就是說
x^x=0
那
x=0就是唯一的解啦
2019-08-11 2:49 pm
x^x = x
x^x - x = 0
x[x^(x - 1) - 1] = 0
x = 0 或x = 1
x = 0 時 0⁰ 無意義
x = 1
不過其中(- 1)²ⁿ = 1，(-1)²ⁿ⁺¹ = -1（n ∈ Z）
x = -1
x = ±1 #
x^x - x = 0
x[x^(x - 1) - 1] = 0
x = 0 或x = 1
x = 0 時 0⁰ 無意義
x = 1
不過其中(- 1)²ⁿ = 1，(-1)²ⁿ⁺¹ = -1（n ∈ Z）
x = -1
x = ±1 #
2020-02-22 9:55 am
x^x = x
=> x = x^(1/x)
=> x^1 = x^(1/x)
=> 1 = 1/x
=> x = 1
But (-1)^(-1) = 1 / (-1)^1 = 1/(-1) = -1
Thus x = 1 or -1
=> x = x^(1/x)
=> x^1 = x^(1/x)
=> 1 = 1/x
=> x = 1
But (-1)^(-1) = 1 / (-1)^1 = 1/(-1) = -1
Thus x = 1 or -1
收錄日期: 2021-04-11 22:56:30
原文連結 [永久失效]:
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