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受欢迎的代数 >

x^{2/3}+x^{1/3}-6=0

解答

x^{\frac{2}{3}} + x^{\frac{1}{3}} - 6 = 0

解答

x = 8, x = - 27

求解步骤

x^{\frac{2}{3}} + x^{\frac{1}{3}} - 6 = 0

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}

(x^{\frac{1}{3}})^{2} + x^{\frac{1}{3}} - 6 = 0

用

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

改写方程式

u^{2} + u - 6 = 0

解

u^{2} + u - 6 = 0 : u = 2, u = - 3

u = 2, u = - 3

代回

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

，求解

x

解

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

解

x^{\frac{1}{3}} = - 3 : x = - 27

x = 8, x = - 27

验证解:

x = 8

真

, x = - 27

真

解为

x = 8, x = - 27

作图

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