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受欢迎的代数 >

x^{12}=12

解答

x^{12} = 12

解答

x = 612, x = - 612, x = 612 i, x = - 612 i, x = 1.06527 \dots + \frac{2.28942 \dots - 0.75654 \dots}{2} i, x = - 1.06527 \dots - \frac{2.28942 \dots - 0.75654 \dots}{2} i, x = - 0.61503 \dots + \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = 0.61503 \dots - \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = 0.61503 \dots + \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = - 0.61503 \dots - \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = - 1.06527 \dots + \frac{2.28942 \dots - 0.75654 \dots}{2} i, x = 1.06527 \dots - \frac{2.28942 \dots - 0.75654 \dots}{2} i

求解步骤

x^{12} = 12

用

u = x^{2}

和

u^{6} = x^{12}

改写方程式

u^{6} = 12

解

u^{6} = 12 : u = 312, u = - 312, u = \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} + 1.31037 \dots i, u = - \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} - 1.31037 \dots i, u = - \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} + 1.31037 \dots i, u = \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} - 1.31037 \dots i

u = 312, u = - 312, u = \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} + 1.31037 \dots i, u = - \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} - 1.31037 \dots i, u = - \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} + 1.31037 \dots i, u = \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} - 1.31037 \dots i

代回

u = x^{2}

，求解

x

解

x^{2} = 312 : x = 612, x = - 612

解

x^{2} = - 312 : x = 612 i, x = - 612 i

解

x^{2} = \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} + 1.31037 \dots i : x = 1.06527 \dots + \frac{2.28942 \dots - 0.75654 \dots}{2} i, x = - 1.06527 \dots - \frac{2.28942 \dots - 0.75654 \dots}{2} i

解

x^{2} = - \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} - 1.31037 \dots i : x = - 0.61503 \dots + \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = 0.61503 \dots - \frac{0.75654 \dots + 2.28942 \dots}{2} i

解

x^{2} = - \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} + 1.31037 \dots i : x = 0.61503 \dots + \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = - 0.61503 \dots - \frac{0.75654 \dots + 2.28942 \dots}{2} i

解

x^{2} = \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} - 1.31037 \dots i : x = - 1.06527 \dots + \frac{2.28942 \dots - 0.75654 \dots}{2} i, x = 1.06527 \dots - \frac{2.28942 \dots - 0.75654 \dots}{2} i

解为

x = 612, x = - 612, x = 612 i, x = - 612 i, x = 1.06527 \dots + \frac{2.28942 \dots - 0.75654 \dots}{2} i, x = - 1.06527 \dots - \frac{2.28942 \dots - 0.75654 \dots}{2} i, x = - 0.61503 \dots + \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = 0.61503 \dots - \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = 0.61503 \dots + \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = - 0.61503 \dots - \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = - 1.06527 \dots + \frac{2.28942 \dots - 0.75654 \dots}{2} i, x = 1.06527 \dots - \frac{2.28942 \dots - 0.75654 \dots}{2} i

作图

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