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受欢迎的代数 >

x^4+x^2+17=0

解答

x^{4} + x^{2} + 17 = 0

解答

x = \frac{- 1 + 2 17}{2} + \frac{67}{2 - 1 + 2 17} i, x = - \frac{- 1 + 2 17}{2} - \frac{67}{2 - 1 + 2 17} i, x = \frac{- 1 + 2 17}{2} - \frac{67}{2 - 1 + 2 17} i, x = - \frac{- 1 + 2 17}{2} + \frac{67}{2 - 1 + 2 17} i

求解步骤

x^{4} + x^{2} + 17 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

u^{2} + u + 17 = 0

解

u^{2} + u + 17 = 0 : u = - \frac{1}{2} + i \frac{67}{2}, u = - \frac{1}{2} - i \frac{67}{2}

u = - \frac{1}{2} + i \frac{67}{2}, u = - \frac{1}{2} - i \frac{67}{2}

代回

u = x^{2}

，求解

x

解

x^{2} = - \frac{1}{2} + i \frac{67}{2} : x = \frac{- 1 + 2 17}{2} + \frac{67}{2 - 1 + 2 17} i, x = - \frac{- 1 + 2 17}{2} - \frac{67}{2 - 1 + 2 17} i

解

x^{2} = - \frac{1}{2} - i \frac{67}{2} : x = \frac{- 1 + 2 17}{2} - \frac{67}{2 - 1 + 2 17} i, x = - \frac{- 1 + 2 17}{2} + \frac{67}{2 - 1 + 2 17} i

解为

x = \frac{- 1 + 2 17}{2} + \frac{67}{2 - 1 + 2 17} i, x = - \frac{- 1 + 2 17}{2} - \frac{67}{2 - 1 + 2 17} i, x = \frac{- 1 + 2 17}{2} - \frac{67}{2 - 1 + 2 17} i, x = - \frac{- 1 + 2 17}{2} + \frac{67}{2 - 1 + 2 17} i

作图

流行的例子

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