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受欢迎的代数 >

3x^6-4x^3-46375=0

解答

3 x^{6} - 4 x^{3} - 46375 = 0

解答

x = 5, x = - \frac{5}{2} + \frac{5 3}{2} i, x = - \frac{5}{2} - \frac{5 3}{2} i, x = - 3 \frac{371}{3}, x = - \frac{3 371 ( - 1 + 3 i )}{2 3 3}, x = - \frac{3 371 ( - 1 - 3 i )}{2 3 3}

求解步骤

3 x^{6} - 4 x^{3} - 46375 = 0

用

u = x^{3}

和

u^{2} = x^{6}

改写方程式

3 u^{2} - 4 u - 46375 = 0

解

3 u^{2} - 4 u - 46375 = 0 : u = 125, u = - \frac{371}{3}

u = 125, u = - \frac{371}{3}

代回

u = x^{3}

，求解

x

解

x^{3} = 125 : x = 5, x = - \frac{5}{2} + \frac{5 3}{2} i, x = - \frac{5}{2} - \frac{5 3}{2} i

解

x^{3} = - \frac{371}{3} : x = - 3 \frac{371}{3}, x = - \frac{3 371 ( - 1 + 3 i )}{2 3 3}, x = - \frac{3 371 ( - 1 - 3 i )}{2 3 3}

解为

x = 5, x = - \frac{5}{2} + \frac{5 3}{2} i, x = - \frac{5}{2} - \frac{5 3}{2} i, x = - 3 \frac{371}{3}, x = - \frac{3 371 ( - 1 + 3 i )}{2 3 3}, x = - \frac{3 371 ( - 1 - 3 i )}{2 3 3}

作图

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