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受欢迎的代数 >

X^4-X^2+1=0

解答

X^{4} - X^{2} + 1 = 0

解答

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

求解步骤

X^{4} - X^{2} + 1 = 0

用

u = X^{2}

和

u^{2} = X^{4}

改写方程式

u^{2} - u + 1 = 0

解

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

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

代回

u = X^{2}

，求解

X

解

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

解

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

解为

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

作图

流行的例子

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