zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

z^4+2z^2=sqrt(3)i

解答

z^{4} + 2 z^{2} = 3 i

解答

z = \frac{1}{2 2 3 - 6 + 2 - 6} + \frac{2 3 - 6 + 2 - 6}{2} i, z = - \frac{1}{2 2 3 - 6 + 2 - 6} - \frac{2 3 - 6 + 2 - 6}{2} i, z = - \frac{1}{2 2 3 + 6 + 6 + 2} + \frac{2 3 + 6 + 6 + 2}{2} i, z = - \frac{1}{2 ( - 2 3 + 6 + 6 + 2 )} - \frac{2 3 + 6 + 6 + 2}{2} i

求解步骤

z^{4} + 2 z^{2} = 3 i

将

3 i

para o lado esquerdo

(z^{4} + 2 z^{2}) - 3 i = 0

改写成标准形式

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

z^{4} + 2 z^{2} - 3 i = 0

用

u = z^{2}

和

u^{2} = z^{4}

改写方程式

u^{2} + 2 u - 3 i = 0

解

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

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

代回

u = z^{2}

，求解

z

解

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

解

z^{2} = - \frac{3 + 2}{2} - \frac{1}{2} i : z = - \frac{1}{2 2 3 + 6 + 6 + 2} + \frac{2 3 + 6 + 6 + 2}{2} i, z = - \frac{1}{2 ( - 2 3 + 6 + 6 + 2 )} - \frac{2 3 + 6 + 6 + 2}{2} i

解为

z = \frac{1}{2 2 3 - 6 + 2 - 6} + \frac{2 3 - 6 + 2 - 6}{2} i, z = - \frac{1}{2 2 3 - 6 + 2 - 6} - \frac{2 3 - 6 + 2 - 6}{2} i, z = - \frac{1}{2 2 3 + 6 + 6 + 2} + \frac{2 3 + 6 + 6 + 2}{2} i, z = - \frac{1}{2 ( - 2 3 + 6 + 6 + 2 )} - \frac{2 3 + 6 + 6 + 2}{2} i

流行的例子

185 = 5 x^{3}

X^{3} - X^{2} - 4 X + 4 = 0

- 3 x^{3} + 2 x^{2} + x = 0

(1+x^2)^2=4(1-x^2)

(1 + x^{2})^{2} = 4 (1 - x^{2})

x^{3} + 6 = 12