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^2(1-z^2)=16

解答

z^{2} (1 - z^{2}) = 16

解答

z = \frac{3}{2} - \frac{7}{2} i, z = - \frac{3}{2} + \frac{7}{2} i, z = \frac{3}{2} + \frac{7}{2} i, z = - \frac{3}{2} - \frac{7}{2} i

求解步骤

z^{2} (1 - z^{2}) = 16

展开

z^{2} (1 - z^{2}) : z^{2} - z^{4}

z^{2} - z^{4} = 16

将

16

para o lado esquerdo

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

改写成标准形式

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

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

用

u = z^{2}

和

u^{2} = z^{4}

改写方程式

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

解

- u^{2} + u - 16 = 0 : u = \frac{1}{2} - i \frac{3 7}{2}, u = \frac{1}{2} + i \frac{3 7}{2}

u = \frac{1}{2} - i \frac{3 7}{2}, u = \frac{1}{2} + i \frac{3 7}{2}

代回

u = z^{2}

，求解

z

解

z^{2} = \frac{1}{2} - i \frac{3 7}{2} : z = \frac{3}{2} - \frac{7}{2} i, z = - \frac{3}{2} + \frac{7}{2} i

解

z^{2} = \frac{1}{2} + i \frac{3 7}{2} : z = \frac{3}{2} + \frac{7}{2} i, z = - \frac{3}{2} - \frac{7}{2} i

解为

z = \frac{3}{2} - \frac{7}{2} i, z = - \frac{3}{2} + \frac{7}{2} i, z = \frac{3}{2} + \frac{7}{2} i, z = - \frac{3}{2} - \frac{7}{2} i

作图

流行的例子

solvefor x,-f=-x^3

so l v e f or x, - f = - x^{3}

-24x-24=x^3+8x^2

- 24 x - 24 = x^{3} + 8 x^{2}

4 x (5 x^{2} - 3) = 0

20x=x^2(x)+36x-2x(x)(x)

20 x = x^{2} (x) + 36 x - 2 x (x) (x)

solvefor y,y^2-y^4=x

so l v e f or y, y^{2} - y^{4} = x