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受欢迎的三角函数 >

30=211.49-20.96cosh(0.03291765x)

解答

30 = 211.49 - 20.96 cosh (0.03291765 x)

解答

x = \frac{8901}{293} ln (\frac{18149 - 324992985}{2096}), x = \frac{8901}{293} ln (\frac{18149 + 324992985}{2096})

+1

度数

x = - 4957.83243 \dots^{\circ}, x = 4957.83243 \dots^{\circ}

求解步骤

30 = 211.49 - 20.96 cosh (0.03291765 x)

交换两边

211.49 - 20.96 cosh (0.03291765 x) = 30

使用三角恒等式改写

211.49 - 20.96 cosh (0.03291765 x) = 30

使用双曲函数恒等式:

cosh (x) = \frac{e ^{x} + e ^{- x}}{2}

211.49 - 20.96 \cdot \frac{e ^{0.03291765 x} + e ^{- 0.03291765 x}}{2} = 30

211.49 - 20.96 \cdot \frac{e ^{0.03291765 x} + e ^{- 0.03291765 x}}{2} = 30

211.49 - 20.96 \cdot \frac{e ^{0.03291765 x} + e ^{- 0.03291765 x}}{2} = 30 : x = \frac{8901}{293} ln (\frac{18149 - 324992985}{2096}), x = \frac{8901}{293} ln (\frac{18149 + 324992985}{2096})

211.49 - 20.96 \cdot \frac{e ^{0.03291765 x} + e ^{- 0.03291765 x}}{2} = 30

使用指数运算法则

211.49 - 20.96 \cdot \frac{e ^{0.03291765 x} + e ^{- 0.03291765 x}}{2} = 30

使用指数法则:

a^{b c} = (a^{b})^{c}

e^{0.03291765 x} = (e^{x})^{0.03291765}, e^{- 0.03291765 x} = (e^{x})^{- 0.03291765}

211.49 - 20.96 \cdot \frac{( e ^{x} ) ^{0.03291765} + ( e ^{x} ) ^{- 0.03291765}}{2} = 30

211.49 - 20.96 \cdot \frac{( e ^{x} ) ^{0.03291765} + ( e ^{x} ) ^{- 0.03291765}}{2} = 30

用

e^{x} = u

改写方程式

211.49 - 20.96 \cdot \frac{( u ) ^{0.03291765} + ( u ) ^{- 0.03291765}}{2} = 30

解

211.49 - 20.96 \cdot \frac{u ^{0.03291765} + u ^{- 0.03291765}}{2} = 30 : u = (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}, u = (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}

211.49 - 20.96 \cdot \frac{u ^{0.03291765} + u ^{- 0.03291765}}{2} = 30

展开

211.49 - 20.96 \cdot \frac{u ^{0.03291765} + u ^{- 0.03291765}}{2} : 211.49 - \frac{20.96 u ^{0.03291765}}{2} - \frac{20.96}{2 u ^{0.03291765}}

211.49 - 20.96 \cdot \frac{u ^{0.03291765} + u ^{- 0.03291765}}{2}

\frac{u ^{0.03291765} + u ^{- 0.03291765}}{2} = \frac{u ^{0.0658353} + 1}{2 u ^{0.03291765}}

\frac{u ^{0.03291765} + u ^{- 0.03291765}}{2}

使用指数法则:

a^{- b} = \frac{1}{a ^{b}}

= \frac{u ^{0.03291765} + \frac{1}{u ^{0.03291765}}}{2}

化简

u^{0.03291765} + \frac{1}{u ^{0.03291765}} : \frac{u ^{0.0658353} + 1}{u ^{0.03291765}}

u^{0.03291765} + \frac{1}{u ^{0.03291765}}

将项转换为分式:

u^{0.03291765} = \frac{u ^{0.03291765} u ^{0.03291765}}{u ^{0.03291765}}

= \frac{u ^{0.03291765} u ^{0.03291765}}{u ^{0.03291765}} + \frac{1}{u ^{0.03291765}}

因为分母相等，所以合并分式:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{u ^{0.03291765} u ^{0.03291765} + 1}{u ^{0.03291765}}

u^{0.03291765} u^{0.03291765} + 1 = u^{0.0658353} + 1

u^{0.03291765} u^{0.03291765} + 1

u^{0.03291765} u^{0.03291765} = u^{0.0658353}

u^{0.03291765} u^{0.03291765}

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

u^{0.03291765} u^{0.03291765} = u^{0.03291765 + 0.03291765}

= u^{0.03291765 + 0.03291765}

数字相加:

0.03291765 + 0.03291765 = 0.0658353

= u^{0.0658353}

= u^{0.0658353} + 1

= \frac{u ^{0.0658353} + 1}{u ^{0.03291765}}

= \frac{\frac{u ^{0.0658353} + 1}{u ^{0.03291765}}}{2}

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{u ^{0.0658353} + 1}{u ^{0.03291765} \cdot 2}

= 211.49 - 20.96 \cdot \frac{u ^{0.0658353} + 1}{2 u ^{0.03291765}}

20.96 \cdot \frac{u ^{0.0658353} + 1}{u ^{0.03291765} \cdot 2} = \frac{20.96 u ^{0.0658353} + 20.96}{2 u ^{0.03291765}}

20.96 \cdot \frac{u ^{0.0658353} + 1}{u ^{0.03291765} \cdot 2}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( u ^{0.0658353} + 1 ) \cdot 20.96}{u ^{0.03291765} \cdot 2}

乘开

(u^{0.0658353} + 1) \cdot 20.96 : 20.96 u^{0.0658353} + 20.96

(u^{0.0658353} + 1) \cdot 20.96

= 20.96 (u^{0.0658353} + 1)

使用分配律:

a (b + c) = ab + a c

a = 20.96, b = u^{0.0658353}, c = 1

= 20.96 u^{0.0658353} + 20.96 \cdot 1

= 20.96 u^{0.0658353} + 1 \cdot 20.96

数字相乘:

1 \cdot 20.96 = 20.96

= 20.96 u^{0.0658353} + 20.96

= \frac{20.96 u ^{0.0658353} + 20.96}{2 u ^{0.03291765}}

= 211.49 - \frac{20.96 u ^{0.0658353} + 20.96}{2 u ^{0.03291765}}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{20.96 u ^{0.0658353} + 20.96}{u ^{0.03291765} \cdot 2} = - (\frac{20.96 u ^{0.0658353}}{u ^{0.03291765} \cdot 2}) - (\frac{20.96}{u ^{0.03291765} \cdot 2})

= 211.49 - (\frac{20.96 u ^{0.0658353}}{2 u ^{0.03291765}}) - (\frac{20.96}{2 u ^{0.03291765}})

去除括号:

(a) = a

= 211.49 - \frac{20.96 u ^{0.0658353}}{u ^{0.03291765} \cdot 2} - \frac{20.96}{u ^{0.03291765} \cdot 2}

消掉

\frac{20.96 u ^{0.0658353}}{u ^{0.03291765} \cdot 2} : \frac{20.96 u ^{0.03291765}}{2}

\frac{20.96 u ^{0.0658353}}{u ^{0.03291765} \cdot 2}

消掉

\frac{20.96 u ^{0.0658353}}{u ^{0.03291765} \cdot 2} : \frac{20.96 u ^{0.03291765}}{2}

\frac{20.96 u ^{0.0658353}}{u ^{0.03291765} \cdot 2}

使用指数法则:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{u ^{0.0658353}}{u ^{0.03291765}} = u^{0.0658353 - 0.03291765}

= \frac{20.96 u ^{0.0658353 - 0.03291765}}{2}

数字相减:

0.0658353 - 0.03291765 = 0.03291765

= \frac{20.96 u ^{0.03291765}}{2}

= \frac{20.96 u ^{0.03291765}}{2}

= 211.49 - \frac{20.96 u ^{0.03291765}}{2} - \frac{20.96}{2 u ^{0.03291765}}

211.49 - \frac{20.96 u ^{0.03291765}}{2} - \frac{20.96}{2 u ^{0.03291765}} = 30

使用以下的指数特性

: a^{n} = (a^{\frac{1}{m}})^{(n \cdot m)}

u^{0.03291765} = (u^{\frac{1}{8901}})^{(0.03291765 \cdot 8901)}

211.49 - \frac{20.96 ( u ^{\frac{1}{8901}} ) ^{293}}{2} - \frac{20.96}{2 ( u ^{\frac{1}{8901}} ) ^{293}} = 30

用

u^{\frac{1}{8901}} = v

改写方程式

211.49 - \frac{20.96 v ^{293}}{2} - \frac{20.96}{2 v ^{293}} = 30

解

211.49 - \frac{20.96 v ^{293}}{2} - \frac{20.96}{2 v ^{293}} = 30 : v = 293 \frac{18149 - 324992985}{2096}, v = 293 \frac{18149 + 324992985}{2096}

211.49 - \frac{20.96 v ^{293}}{2} - \frac{20.96}{2 v ^{293}} = 30

将

211.49

到右边

211.49 - \frac{20.96 v ^{293}}{2} - \frac{20.96}{2 v ^{293}} = 30

两边减去

211.49

211.49 - \frac{20.96 v ^{293}}{2} - \frac{20.96}{2 v ^{293}} - 211.49 = 30 - 211.49

化简

- \frac{20.96 v ^{293}}{2} - \frac{20.96}{2 v ^{293}} = - 181.49

- \frac{20.96 v ^{293}}{2} - \frac{20.96}{2 v ^{293}} = - 181.49

在两边乘以

v^{293}

- \frac{20.96 v ^{293}}{2} - \frac{20.96}{2 v ^{293}} = - 181.49

在两边乘以

v^{293}

- \frac{20.96 v ^{293}}{2} v^{293} - \frac{20.96}{2 v ^{293}} v^{293} = - 181.49 v^{293}

化简

- \frac{20.96 v ^{293}}{2} v^{293} - \frac{20.96}{2 v ^{293}} v^{293} = - 181.49 v^{293}

化简

- \frac{20.96 v ^{293}}{2} v^{293} : - \frac{20.96 v ^{586}}{2}

- \frac{20.96 v ^{293}}{2} v^{293}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{20.96 v ^{293} v ^{293}}{2}

20.96 v^{293} v^{293} = 20.96 v^{586}

20.96 v^{293} v^{293}

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

v^{293} v^{293} = v^{293 + 293}

= 20.96 v^{293 + 293}

数字相加:

293 + 293 = 586

= 20.96 v^{586}

= - \frac{20.96 v ^{586}}{2}

化简

- \frac{20.96}{2 v ^{293}} v^{293} : - \frac{20.96}{2}

- \frac{20.96}{2 v ^{293}} v^{293}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{20.96 v ^{293}}{2 v ^{293}}

约分:

v^{293}

= - \frac{20.96}{2}

- \frac{20.96 v ^{586}}{2} - \frac{20.96}{2} = - 181.49 v^{293}

- \frac{20.96 v ^{586}}{2} - \frac{20.96}{2} = - 181.49 v^{293}

- \frac{20.96 v ^{586}}{2} - \frac{20.96}{2} = - 181.49 v^{293}

解

- \frac{20.96 v ^{586}}{2} - \frac{20.96}{2} = - 181.49 v^{293} : v = 293 \frac{18149 - 324992985}{2096}, v = 293 \frac{18149 + 324992985}{2096}

- \frac{20.96 v ^{586}}{2} - \frac{20.96}{2} = - 181.49 v^{293}

在两边乘以

100

- \frac{20.96 v ^{586}}{2} - \frac{20.96}{2} = - 181.49 v^{293}

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

- \frac{20.96 v ^{586}}{2} \cdot 100 - \frac{20.96}{2} \cdot 100 = - 181.49 v^{293} \cdot 100

整理后得

- 1048 v^{586} - 1048 = - 18149 v^{293}

- 1048 v^{586} - 1048 = - 18149 v^{293}

将

18149 v^{293}

para o lado esquerdo

- 1048 v^{586} - 1048 = - 18149 v^{293}

两边加上

18149 v^{293}

- 1048 v^{586} - 1048 + 18149 v^{293} = - 18149 v^{293} + 18149 v^{293}

化简

- 1048 v^{586} - 1048 + 18149 v^{293} = 0

- 1048 v^{586} - 1048 + 18149 v^{293} = 0

改写成标准形式

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- 1048 v^{586} + 18149 v^{293} - 1048 = 0

用

u = v^{293}

和

u^{2} = v^{586}

改写方程式

- 1048 u^{2} + 18149 u - 1048 = 0

解

- 1048 u^{2} + 18149 u - 1048 = 0 : u = \frac{18149 - 324992985}{2096}, u = \frac{18149 + 324992985}{2096}

- 1048 u^{2} + 18149 u - 1048 = 0

使用求根公式求解

- 1048 u^{2} + 18149 u - 1048 = 0

二次方程求根公式:

若

a = - 1048, b = 18149, c = - 1048

u_{1, 2} = \frac{- 18149 \pm 1814 9 ^{2} - 4 ( - 1048 ) ( - 1048 )}{2 ( - 1048 )}

u_{1, 2} = \frac{- 18149 \pm 1814 9 ^{2} - 4 ( - 1048 ) ( - 1048 )}{2 ( - 1048 )}

1814 9^{2} - 4 (- 1048) (- 1048) = 324992985

1814 9^{2} - 4 (- 1048) (- 1048)

使用法则

- (- a) = a

= 1814 9^{2} - 4 \cdot 1048 \cdot 1048

数字相乘:

4 \cdot 1048 \cdot 1048 = 4393216

= 1814 9^{2} - 4393216

1814 9^{2} = 329386201

= 329386201 - 4393216

数字相减:

329386201 - 4393216 = 324992985

= 324992985

u_{1, 2} = \frac{- 18149 \pm 324992985}{2 ( - 1048 )}

将解分隔开

u_{1} = \frac{- 18149 + 324992985}{2 ( - 1048 )}, u_{2} = \frac{- 18149 - 324992985}{2 ( - 1048 )}

u = \frac{- 18149 + 324992985}{2 ( - 1048 )} : \frac{18149 - 324992985}{2096}

\frac{- 18149 + 324992985}{2 ( - 1048 )}

去除括号:

(- a) = - a

= \frac{- 18149 + 324992985}{- 2 \cdot 1048}

数字相乘:

2 \cdot 1048 = 2096

= \frac{- 18149 + 324992985}{- 2096}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

- 18149 + 324992985 = - (18149 - 324992985)

= \frac{18149 - 324992985}{2096}

u = \frac{- 18149 - 324992985}{2 ( - 1048 )} : \frac{18149 + 324992985}{2096}

\frac{- 18149 - 324992985}{2 ( - 1048 )}

去除括号:

(- a) = - a

= \frac{- 18149 - 324992985}{- 2 \cdot 1048}

数字相乘:

2 \cdot 1048 = 2096

= \frac{- 18149 - 324992985}{- 2096}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

- 18149 - 324992985 = - (18149 + 324992985)

= \frac{18149 + 324992985}{2096}

二次方程组的解是:

u = \frac{18149 - 324992985}{2096}, u = \frac{18149 + 324992985}{2096}

u = \frac{18149 - 324992985}{2096}, u = \frac{18149 + 324992985}{2096}

代回

u = v^{293}

，求解

v

解

v^{293} = \frac{18149 - 324992985}{2096} : v = 293 \frac{18149 - 324992985}{2096}

v^{293} = \frac{18149 - 324992985}{2096}

对于

x^{n} = f (a)

，n 为奇数，解为

x = n f (a)

v = 293 \frac{18149 - 324992985}{2096}

解

v^{293} = \frac{18149 + 324992985}{2096} : v = 293 \frac{18149 + 324992985}{2096}

v^{293} = \frac{18149 + 324992985}{2096}

对于

x^{n} = f (a)

，n 为奇数，解为

x = n f (a)

v = 293 \frac{18149 + 324992985}{2096}

解为

v = 293 \frac{18149 - 324992985}{2096}, v = 293 \frac{18149 + 324992985}{2096}

v = 293 \frac{18149 - 324992985}{2096}, v = 293 \frac{18149 + 324992985}{2096}

验证解

找到无定义的点（奇点）:

v = 0

取

211.49 - \frac{20.96 v ^{293}}{2} - \frac{20.96}{2 v ^{293}}

的分母，令其等于零

解

2 v^{293} = 0 : v = 0

2 v^{293} = 0

两边除以

2

2 v^{293} = 0

两边除以

2

2 v^{293} = 0

两边除以

2

\frac{2 v ^{293}}{2} = \frac{0}{2}

化简

v^{293} = 0

v^{293} = 0

使用法则

x^{n} = 0 \Rightarrow x = 0

v = 0

以下点无定义

v = 0

将不在定义域的点与解相综合:

v = 293 \frac{18149 - 324992985}{2096}, v = 293 \frac{18149 + 324992985}{2096}

v = 293 \frac{18149 - 324992985}{2096}, v = 293 \frac{18149 + 324992985}{2096}

代回

v = u^{\frac{1}{8901}}

，求解

u

解

u^{\frac{1}{8901}} = 293 \frac{18149 - 324992985}{2096} : u = (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}

u^{\frac{1}{8901}} = 293 \frac{18149 - 324992985}{2096}

对方程式两边

8901

次方:

u = (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}

u^{\frac{1}{8901}} = 293 \frac{18149 - 324992985}{2096}

(u^{\frac{1}{8901}})^{8901} = 293 \frac{18149 - 324992985}{2096}^{8901}

展开

(u^{\frac{1}{8901}})^{8901} : u

(u^{\frac{1}{8901}})^{8901}

使用指数法则:

(a^{b})^{c} = a^{b c}

= u^{\frac{1}{8901} \cdot 8901}

\frac{1}{8901} \cdot 8901 = 1

\frac{1}{8901} \cdot 8901

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 8901}{8901}

约分:

8901

= 1

= u

展开

293 \frac{18149 - 324992985}{2096}^{8901} : (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}

293 \frac{18149 - 324992985}{2096}^{8901}

使用根式运算法则:

n a = a^{\frac{1}{n}}

= (\frac{18149 - 324992985}{2096})^{\frac{1}{293}}^{8901}

使用指数法则:

(a^{b})^{c} = a^{b c}

= (\frac{18149 - 324992985}{2096})^{\frac{1}{293} \cdot 8901}

\frac{1}{293} \cdot 8901 = \frac{8901}{293}

\frac{1}{293} \cdot 8901

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 8901}{293}

数字相乘:

1 \cdot 8901 = 8901

= \frac{8901}{293}

= (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}

u = (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}

u = (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}

验证解:

u = (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}

真

将它们代入

u^{\frac{1}{8901}} = 293 \frac{18149 - 324992985}{2096}

检验解是否符合

去除与方程不符的解。

代入

u = (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}} :

真

(\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}^{\frac{1}{8901}} = 293 \frac{18149 - 324992985}{2096}

(\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}^{\frac{1}{8901}} = 293 \frac{18149 - 324992985}{2096}

(\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}^{\frac{1}{8901}}

使用指数法则:

(a^{b})^{c} = a^{b c}

= (\frac{18149 - 324992985}{2096})^{\frac{8901}{293} \cdot \frac{1}{8901}}

整理后得

= (\frac{18149 - 324992985}{2096})^{\frac{1}{293}}

a^{\frac{1}{n}} = n a

= 293 \frac{18149 - 324992985}{2096}

293 \frac{18149 - 324992985}{2096} = 293 \frac{18149 - 324992985}{2096}

真

解是

u = (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}

解

u^{\frac{1}{8901}} = 293 \frac{18149 + 324992985}{2096} : u = (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}

u^{\frac{1}{8901}} = 293 \frac{18149 + 324992985}{2096}

对方程式两边

8901

次方:

u = (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}

u^{\frac{1}{8901}} = 293 \frac{18149 + 324992985}{2096}

(u^{\frac{1}{8901}})^{8901} = 293 \frac{18149 + 324992985}{2096}^{8901}

展开

(u^{\frac{1}{8901}})^{8901} : u

(u^{\frac{1}{8901}})^{8901}

使用指数法则:

(a^{b})^{c} = a^{b c}

= u^{\frac{1}{8901} \cdot 8901}

\frac{1}{8901} \cdot 8901 = 1

\frac{1}{8901} \cdot 8901

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 8901}{8901}

约分:

8901

= 1

= u

展开

293 \frac{18149 + 324992985}{2096}^{8901} : (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}

293 \frac{18149 + 324992985}{2096}^{8901}

使用根式运算法则:

n a = a^{\frac{1}{n}}

= (\frac{18149 + 324992985}{2096})^{\frac{1}{293}}^{8901}

使用指数法则:

(a^{b})^{c} = a^{b c}

= (\frac{18149 + 324992985}{2096})^{\frac{1}{293} \cdot 8901}

\frac{1}{293} \cdot 8901 = \frac{8901}{293}

\frac{1}{293} \cdot 8901

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 8901}{293}

数字相乘:

1 \cdot 8901 = 8901

= \frac{8901}{293}

= (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}

u = (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}

u = (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}

验证解:

u = (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}

真

将它们代入

u^{\frac{1}{8901}} = 293 \frac{18149 + 324992985}{2096}

检验解是否符合

去除与方程不符的解。

代入

u = (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}} :

真

(\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}^{\frac{1}{8901}} = 293 \frac{18149 + 324992985}{2096}

(\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}^{\frac{1}{8901}} = 293 \frac{18149 + 324992985}{2096}

(\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}^{\frac{1}{8901}}

使用指数法则:

(a^{b})^{c} = a^{b c}

= (\frac{18149 + 324992985}{2096})^{\frac{8901}{293} \cdot \frac{1}{8901}}

整理后得

= (\frac{18149 + 324992985}{2096})^{\frac{1}{293}}

a^{\frac{1}{n}} = n a

= 293 \frac{18149 + 324992985}{2096}

293 \frac{18149 + 324992985}{2096} = 293 \frac{18149 + 324992985}{2096}

真

解是

u = (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}

u = (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}, u = (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}

验证解:

u = (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}

真

, u = (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}

真

将它们代入

211.49 - 20.96 \frac{u ^{0.03291765} + u ^{- 0.03291765}}{2} = 30

检验解是否符合

去除与方程不符的解。

代入

u = (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}} :

真

211.49 - 20.96 \cdot \frac{( ( \frac{18149 - 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{18149 - 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2} = 30

211.49 - 20.96 \cdot \frac{( ( \frac{18149 - 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{18149 - 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2} = 29.99999 \dots

211.49 - 20.96 \cdot \frac{( ( \frac{18149 - 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{18149 - 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2}

\frac{( ( \frac{18149 - 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{18149 - 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2} = \frac{17.31774 \dots}{2}

\frac{( ( \frac{18149 - 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{18149 - 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2}

(\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}^{0.03291765} = 0.05793 \dots

(\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}^{0.03291765}

使用指数法则:

(a^{b})^{c} = a^{b c}

= (\frac{18149 - 324992985}{2096})^{\frac{8901}{293} \cdot 0.03291765}

\frac{8901}{293} \cdot 0.03291765 = 1.00000 \dots

\frac{8901}{293} \cdot 0.03291765

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{8901 \cdot 0.03291765}{293}

数字相乘:

8901 \cdot 0.03291765 = 293.00000 \dots

= \frac{293.00000 \dots}{293}

数字相除:

\frac{293.00000 \dots}{293} = 1.00000 \dots

= 1.00000 \dots

= (\frac{18149 - 324992985}{2096})^{1.00000 \dots}

\frac{18149 - 324992985}{2096} = \frac{121.43818 \dots}{2096}

\frac{18149 - 324992985}{2096}

转换为小数形式

324992985 = 18027.56181 \dots

= \frac{18149 - 18027.56181 \dots}{2096}

数字相减:

18149 - 18027.56181 \dots = 121.43818 \dots

= \frac{121.43818 \dots}{2096}

= (\frac{121.43818 \dots}{2096})^{1.00000 \dots}

数字相除:

\frac{121.43818 \dots}{2096} = 0.05793 \dots

= 0.05793 \dots^{1.00000 \dots}

0.05793 \dots^{1.00000 \dots} = 0.05793 \dots

= 0.05793 \dots

(\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}^{- 0.03291765} = 17.25981 \dots

(\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}^{- 0.03291765}

使用指数法则:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{( ( \frac{18149 - 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765}}

(\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}^{0.03291765} : (\frac{18149 - 324992985}{2096})^{1.00000 \dots}

使用指数法则:

(a^{b})^{c} = a^{b c}

= (\frac{18149 - 324992985}{2096})^{\frac{8901}{293} \cdot 0.03291765}

\frac{8901}{293} \cdot 0.03291765 = 1.00000 \dots

\frac{8901}{293} \cdot 0.03291765

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{8901 \cdot 0.03291765}{293}

数字相乘:

8901 \cdot 0.03291765 = 293.00000 \dots

= \frac{293.00000 \dots}{293}

数字相除:

\frac{293.00000 \dots}{293} = 1.00000 \dots

= 1.00000 \dots

= (\frac{18149 - 324992985}{2096})^{1.00000 \dots}

= \frac{1}{( \frac{18149 - 324992985}{2096} ) ^{1.00000 \dots}}

\frac{18149 - 324992985}{2096} = \frac{121.43818 \dots}{2096}

\frac{18149 - 324992985}{2096}

转换为小数形式

324992985 = 18027.56181 \dots

= \frac{18149 - 18027.56181 \dots}{2096}

数字相减:

18149 - 18027.56181 \dots = 121.43818 \dots

= \frac{121.43818 \dots}{2096}

= \frac{1}{( \frac{121.43818 \dots}{2096} ) ^{1.00000 \dots}}

(\frac{121.43818 \dots}{2096})^{1.00000 \dots} = 0.05793 \dots

= \frac{1}{0.05793 \dots}

数字相除:

\frac{1}{0.05793 \dots} = 17.25981 \dots

= 17.25981 \dots

= \frac{0.05793 \dots + 17.25981 \dots}{2}

数字相加:

0.05793 \dots + 17.25981 \dots = 17.31774 \dots

= \frac{17.31774 \dots}{2}

= 211.49 - 20.96 \cdot \frac{17.31774 \dots}{2}

20.96 \cdot \frac{17.31774 \dots}{2} = 181.49000 \dots

20.96 \cdot \frac{17.31774 \dots}{2}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{17.31774 \dots \cdot 20.96}{2}

数字相乘:

17.31774 \dots \cdot 20.96 = 362.98000 \dots

= \frac{362.98000 \dots}{2}

数字相除:

\frac{362.98000 \dots}{2} = 181.49000 \dots

= 181.49000 \dots

= 211.49 - 181.49000 \dots

数字相减:

211.49 - 181.49000 \dots = 29.99999 \dots

= 29.99999 \dots

29.99999 \dots = 30

真

代入

u = (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}} :

真

211.49 - 20.96 \cdot \frac{( ( \frac{18149 + 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{18149 + 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2} = 30

211.49 - 20.96 \cdot \frac{( ( \frac{18149 + 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{18149 + 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2} = 29.99999 \dots

211.49 - 20.96 \cdot \frac{( ( \frac{18149 + 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{18149 + 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2}

\frac{( ( \frac{18149 + 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{18149 + 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2} = \frac{17.31774 \dots}{2}

\frac{( ( \frac{18149 + 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{18149 + 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2}

(\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}^{0.03291765} = 17.25981 \dots

(\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}^{0.03291765}

使用指数法则:

(a^{b})^{c} = a^{b c}

= (\frac{18149 + 324992985}{2096})^{\frac{8901}{293} \cdot 0.03291765}

\frac{8901}{293} \cdot 0.03291765 = 1.00000 \dots

\frac{8901}{293} \cdot 0.03291765

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{8901 \cdot 0.03291765}{293}

数字相乘:

8901 \cdot 0.03291765 = 293.00000 \dots

= \frac{293.00000 \dots}{293}

数字相除:

\frac{293.00000 \dots}{293} = 1.00000 \dots

= 1.00000 \dots

= (\frac{18149 + 324992985}{2096})^{1.00000 \dots}

\frac{18149 + 324992985}{2096} = \frac{36176.56181 \dots}{2096}

\frac{18149 + 324992985}{2096}

转换为小数形式

324992985 = 18027.56181 \dots

= \frac{18149 + 18027.56181 \dots}{2096}

数字相加:

18149 + 18027.56181 \dots = 36176.56181 \dots

= \frac{36176.56181 \dots}{2096}

= (\frac{36176.56181 \dots}{2096})^{1.00000 \dots}

数字相除:

\frac{36176.56181 \dots}{2096} = 17.25981 \dots

= 17.25981 \dots^{1.00000 \dots}

17.25981 \dots^{1.00000 \dots} = 17.25981 \dots

= 17.25981 \dots

(\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}^{- 0.03291765} = 0.05793 \dots

(\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}^{- 0.03291765}

使用指数法则:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{( ( \frac{18149 + 324992985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765}}

(\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}^{0.03291765} : (\frac{18149 + 324992985}{2096})^{1.00000 \dots}

使用指数法则:

(a^{b})^{c} = a^{b c}

= (\frac{18149 + 324992985}{2096})^{\frac{8901}{293} \cdot 0.03291765}

\frac{8901}{293} \cdot 0.03291765 = 1.00000 \dots

\frac{8901}{293} \cdot 0.03291765

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{8901 \cdot 0.03291765}{293}

数字相乘:

8901 \cdot 0.03291765 = 293.00000 \dots

= \frac{293.00000 \dots}{293}

数字相除:

\frac{293.00000 \dots}{293} = 1.00000 \dots

= 1.00000 \dots

= (\frac{18149 + 324992985}{2096})^{1.00000 \dots}

= \frac{1}{( \frac{18149 + 324992985}{2096} ) ^{1.00000 \dots}}

\frac{18149 + 324992985}{2096} = \frac{36176.56181 \dots}{2096}

\frac{18149 + 324992985}{2096}

转换为小数形式

324992985 = 18027.56181 \dots

= \frac{18149 + 18027.56181 \dots}{2096}

数字相加:

18149 + 18027.56181 \dots = 36176.56181 \dots

= \frac{36176.56181 \dots}{2096}

= \frac{1}{( \frac{36176.56181 \dots}{2096} ) ^{1.00000 \dots}}

(\frac{36176.56181 \dots}{2096})^{1.00000 \dots} = 17.25981 \dots

= \frac{1}{17.25981 \dots}

数字相除:

\frac{1}{17.25981 \dots} = 0.05793 \dots

= 0.05793 \dots

= \frac{17.25981 \dots + 0.05793 \dots}{2}

数字相加:

17.25981 \dots + 0.05793 \dots = 17.31774 \dots

= \frac{17.31774 \dots}{2}

= 211.49 - 20.96 \cdot \frac{17.31774 \dots}{2}

20.96 \cdot \frac{17.31774 \dots}{2} = 181.49000 \dots

20.96 \cdot \frac{17.31774 \dots}{2}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{17.31774 \dots \cdot 20.96}{2}

数字相乘:

17.31774 \dots \cdot 20.96 = 362.98000 \dots

= \frac{362.98000 \dots}{2}

数字相除:

\frac{362.98000 \dots}{2} = 181.49000 \dots

= 181.49000 \dots

= 211.49 - 181.49000 \dots

数字相减:

211.49 - 181.49000 \dots = 29.99999 \dots

= 29.99999 \dots

29.99999 \dots = 30

真

解为

u = (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}, u = (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}

u = (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}, u = (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}

代回

u = e^{x}

，求解

x

解

e^{x} = (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}} : x = \frac{8901}{293} ln (\frac{18149 - 324992985}{2096})

e^{x} = (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}

使用指数运算法则

e^{x} = (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}

若

f (x) = g (x)

，则

ln (f (x)) = ln (g (x))

ln (e^{x}) = ln (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}

使用对数计算法则:

ln (e^{a}) = a

ln (e^{x}) = x

x = ln (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}}

使用对数计算法则:

ln (x^{a}) = a \cdot ln (x)

ln (\frac{18149 - 324992985}{2096})^{\frac{8901}{293}} = \frac{8901}{293} ln (\frac{18149 - 324992985}{2096})

x = \frac{8901}{293} ln (\frac{18149 - 324992985}{2096})

x = \frac{8901}{293} ln (\frac{18149 - 324992985}{2096})

解

e^{x} = (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}} : x = \frac{8901}{293} ln (\frac{18149 + 324992985}{2096})

e^{x} = (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}

使用指数运算法则

e^{x} = (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}

若

f (x) = g (x)

，则

ln (f (x)) = ln (g (x))

ln (e^{x}) = ln (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}

使用对数计算法则:

ln (e^{a}) = a

ln (e^{x}) = x

x = ln (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}}

使用对数计算法则:

ln (x^{a}) = a \cdot ln (x)

ln (\frac{18149 + 324992985}{2096})^{\frac{8901}{293}} = \frac{8901}{293} ln (\frac{18149 + 324992985}{2096})

x = \frac{8901}{293} ln (\frac{18149 + 324992985}{2096})

x = \frac{8901}{293} ln (\frac{18149 + 324992985}{2096})

x = \frac{8901}{293} ln (\frac{18149 - 324992985}{2096}), x = \frac{8901}{293} ln (\frac{18149 + 324992985}{2096})

x = \frac{8901}{293} ln (\frac{18149 - 324992985}{2096}), x = \frac{8901}{293} ln (\frac{18149 + 324992985}{2096})

作图

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