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受欢迎的代数 >

x^4-128x^{13/5}=0

解答

x^{4} - 128 x^{\frac{13}{5}} = 0

解答

x = 0, x = 32

求解步骤

x^{4} - 128 x^{\frac{13}{5}} = 0

使用以下的指数特性

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

x^{4} = (x^{\frac{1}{5}})^{(4 \cdot 5)}

使用以下的指数特性

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

x^{\frac{13}{5}} = (x^{\frac{1}{5}})^{13}

(x^{\frac{1}{5}})^{20} - 128 (x^{\frac{1}{5}})^{13} = 0

用

x^{\frac{1}{5}} = u

改写方程式

u^{20} - 128 u^{13} = 0

解

u^{20} - 128 u^{13} = 0 : u = 0, u = 2

u = 0, u = 2

代回

u = x^{\frac{1}{5}}

，求解

x

解

x^{\frac{1}{5}} = 0 : x = 0

解

x^{\frac{1}{5}} = 2 : x = 32

x = 0, x = 32

验证解:

x = 0

真

, x = 32

真

解为

x = 0, x = 32

作图

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