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受欢迎的代数 >

3x^{1/3}+2x^{2/3}=5

解答

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

解答

x = 1, x = - \frac{125}{8}

+1

十进制

x = 1, x = - 15.625

求解步骤

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

使用以下的指数特性

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

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

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

用

x^{\frac{1}{3}} = u

改写方程式

3 u + 2 u^{2} = 5

解

3 u + 2 u^{2} = 5 : u = 1, u = - \frac{5}{2}

u = 1, u = - \frac{5}{2}

代回

u = x^{\frac{1}{3}}

，求解

x

解

x^{\frac{1}{3}} = 1 : x = 1

解

x^{\frac{1}{3}} = - \frac{5}{2} : x = - \frac{125}{8}

x = 1, x = - \frac{125}{8}

验证解:

x = 1

真

, x = - \frac{125}{8}

真

解为

x = 1, x = - \frac{125}{8}

作图

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