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受欢迎的代数 >

x^6-5x^3-16=0

解答

x^{6} - 5 x^{3} - 16 = 0

解答

x = 3 \frac{5 + 89}{2}, x = - 3 \frac{5 + 89}{2} \frac{1}{2} + 3 \frac{5 + 89}{2} \frac{3}{2} i, x = - 3 \frac{5 + 89}{2} \frac{1}{2} - 3 \frac{5 + 89}{2} \frac{3}{2} i, x = 3 \frac{5 - 89}{2}, x = - 3 \frac{5 - 89}{2} \frac{1}{2} + 3 \frac{5 - 89}{2} \frac{3}{2} i, x = - 3 \frac{5 - 89}{2} \frac{1}{2} - 3 \frac{5 - 89}{2} \frac{3}{2} i

求解步骤

x^{6} - 5 x^{3} - 16 = 0

用

u = x^{3}

和

u^{2} = x^{6}

改写方程式

u^{2} - 5 u - 16 = 0

解

u^{2} - 5 u - 16 = 0 : u = \frac{5 + 89}{2}, u = \frac{5 - 89}{2}

u = \frac{5 + 89}{2}, u = \frac{5 - 89}{2}

代回

u = x^{3}

，求解

x

解

x^{3} = \frac{5 + 89}{2} : x = 3 \frac{5 + 89}{2}, x = - 3 \frac{5 + 89}{2} \frac{1}{2} + 3 \frac{5 + 89}{2} \frac{3}{2} i, x = - 3 \frac{5 + 89}{2} \frac{1}{2} - 3 \frac{5 + 89}{2} \frac{3}{2} i

解

x^{3} = \frac{5 - 89}{2} : x = 3 \frac{5 - 89}{2}, x = - 3 \frac{5 - 89}{2} \frac{1}{2} + 3 \frac{5 - 89}{2} \frac{3}{2} i, x = - 3 \frac{5 - 89}{2} \frac{1}{2} - 3 \frac{5 - 89}{2} \frac{3}{2} i

解为

x = 3 \frac{5 + 89}{2}, x = - 3 \frac{5 + 89}{2} \frac{1}{2} + 3 \frac{5 + 89}{2} \frac{3}{2} i, x = - 3 \frac{5 + 89}{2} \frac{1}{2} - 3 \frac{5 + 89}{2} \frac{3}{2} i, x = 3 \frac{5 - 89}{2}, x = - 3 \frac{5 - 89}{2} \frac{1}{2} + 3 \frac{5 - 89}{2} \frac{3}{2} i, x = - 3 \frac{5 - 89}{2} \frac{1}{2} - 3 \frac{5 - 89}{2} \frac{3}{2} i

作图

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