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受欢迎的代数 >

16z^4-4z^2+1=0

解答

16 z^{4} - 4 z^{2} + 1 = 0

解答

z = \frac{3}{4} + \frac{1}{4} i, z = - \frac{3}{4} - \frac{1}{4} i, z = \frac{3}{4} - \frac{1}{4} i, z = - \frac{3}{4} + \frac{1}{4} i

求解步骤

16 z^{4} - 4 z^{2} + 1 = 0

用

u = z^{2}

和

u^{2} = z^{4}

改写方程式

16 u^{2} - 4 u + 1 = 0

解

16 u^{2} - 4 u + 1 = 0 : u = \frac{1}{8} + i \frac{3}{8}, u = \frac{1}{8} - i \frac{3}{8}

u = \frac{1}{8} + i \frac{3}{8}, u = \frac{1}{8} - i \frac{3}{8}

代回

u = z^{2}

，求解

z

解

z^{2} = \frac{1}{8} + i \frac{3}{8} : z = \frac{3}{4} + \frac{1}{4} i, z = - \frac{3}{4} - \frac{1}{4} i

解

z^{2} = \frac{1}{8} - i \frac{3}{8} : z = \frac{3}{4} - \frac{1}{4} i, z = - \frac{3}{4} + \frac{1}{4} i

解为

z = \frac{3}{4} + \frac{1}{4} i, z = - \frac{3}{4} - \frac{1}{4} i, z = \frac{3}{4} - \frac{1}{4} i, z = - \frac{3}{4} + \frac{1}{4} i

作图

流行的例子

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5 x^{3} - 27 x^{2} - 17 x - 6 = 0

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- x^{4} - 8 x^{3} + 7 x^{2} + 56 x = 0

30x-4x^2-2x^3=0

30 x - 4 x^{2} - 2 x^{3} = 0

-λ^3+5λ^2-3λ-9=0

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