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受欢迎的代数 >

x^4-x^2+9=0

解答

x^{4} - x^{2} + 9 = 0

解答

x = \frac{7}{2} + \frac{5}{2} i, x = - \frac{7}{2} - \frac{5}{2} i, x = \frac{7}{2} - \frac{5}{2} i, x = - \frac{7}{2} + \frac{5}{2} i

求解步骤

x^{4} - x^{2} + 9 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

u^{2} - u + 9 = 0

解

u^{2} - u + 9 = 0 : u = \frac{1}{2} + i \frac{35}{2}, u = \frac{1}{2} - i \frac{35}{2}

u = \frac{1}{2} + i \frac{35}{2}, u = \frac{1}{2} - i \frac{35}{2}

代回

u = x^{2}

，求解

x

解

x^{2} = \frac{1}{2} + i \frac{35}{2} : x = \frac{7}{2} + \frac{5}{2} i, x = - \frac{7}{2} - \frac{5}{2} i

解

x^{2} = \frac{1}{2} - i \frac{35}{2} : x = \frac{7}{2} - \frac{5}{2} i, x = - \frac{7}{2} + \frac{5}{2} i

解为

x = \frac{7}{2} + \frac{5}{2} i, x = - \frac{7}{2} - \frac{5}{2} i, x = \frac{7}{2} - \frac{5}{2} i, x = - \frac{7}{2} + \frac{5}{2} i

作图

流行的例子

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