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受欢迎的代数 >

x^2+2x^8=0

解答

x^{2} + 2 x^{8} = 0

解答

x = 0, x = - \frac{1}{3 2}, x = - - \frac{1}{3 2}, x = \frac{3}{2 6 2} - \frac{6 2 \frac{3}{2 3 2}}{3} i, x = - \frac{3}{2 6 2} + \frac{6 2 \frac{3}{2 3 2}}{3} i, x = \frac{3}{2 6 2} + \frac{1}{2 ^{\frac{7}{6}}} i, x = - \frac{3}{2 6 2} - \frac{1}{2 6 2} i

求解步骤

x^{2} + 2 x^{8} = 0

改写成标准形式

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

2 x^{8} + x^{2} = 0

用

u = x^{2}

和

u^{4} = x^{8}

改写方程式

2 u^{4} + u = 0

解

2 u^{4} + u = 0 : u = 0, u = - \frac{1}{3 2}, u = \frac{1}{2 3 2} - \frac{3}{2 3 2} i, u = \frac{1}{2 3 2} + \frac{3}{2 3 2} i

u = 0, u = - \frac{1}{3 2}, u = \frac{1}{2 3 2} - \frac{3}{2 3 2} i, u = \frac{1}{2 3 2} + \frac{3}{2 3 2} i

代回

u = x^{2}

，求解

x

解

x^{2} = 0 : x = 0

解

x^{2} = - \frac{1}{3 2} : x = - \frac{1}{3 2}, x = - - \frac{1}{3 2}

解

x^{2} = \frac{1}{2 3 2} - \frac{3}{2 3 2} i : x = \frac{3}{2 6 2} - \frac{6 2 \frac{3}{2 3 2}}{3} i, x = - \frac{3}{2 6 2} + \frac{6 2 \frac{3}{2 3 2}}{3} i

解

x^{2} = \frac{1}{2 3 2} + \frac{3}{2 3 2} i : x = \frac{3}{2 6 2} + \frac{1}{2 ^{\frac{7}{6}}} i, x = - \frac{3}{2 6 2} - \frac{1}{2 6 2} i

解为

x = 0, x = - \frac{1}{3 2}, x = - - \frac{1}{3 2}, x = \frac{3}{2 6 2} - \frac{6 2 \frac{3}{2 3 2}}{3} i, x = - \frac{3}{2 6 2} + \frac{6 2 \frac{3}{2 3 2}}{3} i, x = \frac{3}{2 6 2} + \frac{1}{2 ^{\frac{7}{6}}} i, x = - \frac{3}{2 6 2} - \frac{1}{2 6 2} i

作图

流行的例子

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