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受欢迎的代数 >

x^{12}=832

解答

x^{12} = 832

解答

x = 21213, x = - 21213, x = 21213 i, x = - 21213 i, x = - 0.87561 \dots + \frac{1.53340 \dots + 9.40533 \dots}{2} i, x = 0.87561 \dots - \frac{1.53340 \dots + 9.40533 \dots}{2} i, x = 1.51661 \dots + \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = - 1.51661 \dots - \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = - 1.51661 \dots + \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = 1.51661 \dots - \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = 0.87561 \dots + \frac{1.53340 \dots + 9.40533 \dots}{2} i, x = - 0.87561 \dots - \frac{1.53340 \dots + 9.40533 \dots}{2} i

求解步骤

x^{12} = 832

用

u = x^{2}

和

u^{6} = x^{12}

改写方程式

u^{6} = 832

解

u^{6} = 832 : u = 2613, u = - 2613, u = - 1.53340 \dots - 2.65593 \dots i, u = 1.53340 \dots + 2.65593 \dots i, u = 1.53340 \dots - 2.65593 \dots i, u = - 1.53340 \dots + 2.65593 \dots i

u = 2613, u = - 2613, u = - 1.53340 \dots - 2.65593 \dots i, u = 1.53340 \dots + 2.65593 \dots i, u = 1.53340 \dots - 2.65593 \dots i, u = - 1.53340 \dots + 2.65593 \dots i

代回

u = x^{2}

，求解

x

解

x^{2} = 2613 : x = 21213, x = - 21213

解

x^{2} = - 2613 : x = 21213 i, x = - 21213 i

解

x^{2} = - 1.53340 \dots - 2.65593 \dots i : x = - 0.87561 \dots + \frac{1.53340 \dots + 9.40533 \dots}{2} i, x = 0.87561 \dots - \frac{1.53340 \dots + 9.40533 \dots}{2} i

解

x^{2} = 1.53340 \dots + 2.65593 \dots i : x = 1.51661 \dots + \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = - 1.51661 \dots - \frac{9.40533 \dots - 1.53340 \dots}{2} i

解

x^{2} = 1.53340 \dots - 2.65593 \dots i : x = - 1.51661 \dots + \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = 1.51661 \dots - \frac{9.40533 \dots - 1.53340 \dots}{2} i

解

x^{2} = - 1.53340 \dots + 2.65593 \dots i : x = 0.87561 \dots + \frac{1.53340 \dots + 9.40533 \dots}{2} i, x = - 0.87561 \dots - \frac{1.53340 \dots + 9.40533 \dots}{2} i

解为

x = 21213, x = - 21213, x = 21213 i, x = - 21213 i, x = - 0.87561 \dots + \frac{1.53340 \dots + 9.40533 \dots}{2} i, x = 0.87561 \dots - \frac{1.53340 \dots + 9.40533 \dots}{2} i, x = 1.51661 \dots + \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = - 1.51661 \dots - \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = - 1.51661 \dots + \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = 1.51661 \dots - \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = 0.87561 \dots + \frac{1.53340 \dots + 9.40533 \dots}{2} i, x = - 0.87561 \dots - \frac{1.53340 \dots + 9.40533 \dots}{2} i

作图

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