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受欢迎的代数 >

x^{12}-1=4

解答

x^{12} - 1 = 4

解答

x = 65, x = - 65, x = 65 i, x = - 65 i, x = 0.99032 \dots + \frac{1.70997 \dots - 0.65383 \dots}{2} i, x = - 0.99032 \dots - \frac{1.70997 \dots - 0.65383 \dots}{2} i, x = - 0.57176 \dots + \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = 0.57176 \dots - \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = 0.57176 \dots + \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = - 0.57176 \dots - \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = - 0.99032 \dots + \frac{1.70997 \dots - 0.65383 \dots}{2} i, x = 0.99032 \dots - \frac{1.70997 \dots - 0.65383 \dots}{2} i

求解步骤

x^{12} - 1 = 4

将

1

到右边

x^{12} = 5

用

u = x^{2}

和

u^{6} = x^{12}

改写方程式

u^{6} = 5

解

u^{6} = 5 : u = 35, u = - 35, u = 0.65383 \dots + 1.13246 \dots i, u = - 0.65383 \dots - 1.13246 \dots i, u = - 0.65383 \dots + 1.13246 \dots i, u = 0.65383 \dots - 1.13246 \dots i

u = 35, u = - 35, u = 0.65383 \dots + 1.13246 \dots i, u = - 0.65383 \dots - 1.13246 \dots i, u = - 0.65383 \dots + 1.13246 \dots i, u = 0.65383 \dots - 1.13246 \dots i

代回

u = x^{2}

，求解

x

解

x^{2} = 35 : x = 65, x = - 65

解

x^{2} = - 35 : x = 65 i, x = - 65 i

解

x^{2} = 0.65383 \dots + 1.13246 \dots i : x = 0.99032 \dots + \frac{1.70997 \dots - 0.65383 \dots}{2} i, x = - 0.99032 \dots - \frac{1.70997 \dots - 0.65383 \dots}{2} i

解

x^{2} = - 0.65383 \dots - 1.13246 \dots i : x = - 0.57176 \dots + \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = 0.57176 \dots - \frac{0.65383 \dots + 1.70997 \dots}{2} i

解

x^{2} = - 0.65383 \dots + 1.13246 \dots i : x = 0.57176 \dots + \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = - 0.57176 \dots - \frac{0.65383 \dots + 1.70997 \dots}{2} i

解

x^{2} = 0.65383 \dots - 1.13246 \dots i : x = - 0.99032 \dots + \frac{1.70997 \dots - 0.65383 \dots}{2} i, x = 0.99032 \dots - \frac{1.70997 \dots - 0.65383 \dots}{2} i

解为

x = 65, x = - 65, x = 65 i, x = - 65 i, x = 0.99032 \dots + \frac{1.70997 \dots - 0.65383 \dots}{2} i, x = - 0.99032 \dots - \frac{1.70997 \dots - 0.65383 \dots}{2} i, x = - 0.57176 \dots + \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = 0.57176 \dots - \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = 0.57176 \dots + \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = - 0.57176 \dots - \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = - 0.99032 \dots + \frac{1.70997 \dots - 0.65383 \dots}{2} i, x = 0.99032 \dots - \frac{1.70997 \dots - 0.65383 \dots}{2} i

作图

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