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受欢迎的代数 >

x^{2/5}+3x^{1/5}-4=0

解答

x^{\frac{2}{5}} + 3 x^{\frac{1}{5}} - 4 = 0

解答

x = 1, x = - 1024

求解步骤

x^{\frac{2}{5}} + 3 x^{\frac{1}{5}} - 4 = 0

使用以下的指数特性

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

x^{\frac{2}{5}} = (x^{\frac{1}{5}})^{2}

(x^{\frac{1}{5}})^{2} + 3 x^{\frac{1}{5}} - 4 = 0

用

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

改写方程式

u^{2} + 3 u - 4 = 0

解

u^{2} + 3 u - 4 = 0 : u = 1, u = - 4

u = 1, u = - 4

代回

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

，求解

x

解

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

解

x^{\frac{1}{5}} = - 4 : x = - 1024

x = 1, x = - 1024

验证解:

x = 1

真

, x = - 1024

真

解为

x = 1, x = - 1024

作图

流行的例子

x + 5 = x - 7

8 = 14 - 5 x

sqrt(2x+7)-sqrt(x-3)=1

2 x + 7 - x - 3 = 1

\sqrt[3]{x}-4\sqrt[6]{x}=32

3 x - 4 6 x = 32

(x+1)^{3/2}-2=25

(x + 1)^{\frac{3}{2}} - 2 = 25