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 >

(-2x^4+3x^2-5)=(x-x)

解答

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

解答

x = \frac{3 + 2 10}{2 2} - \frac{31}{2 2 3 + 2 10} i, x = - \frac{3 + 2 10}{2 2} + \frac{31}{2 2 3 + 2 10} i, x = \frac{3 + 2 10}{2 2} + \frac{31}{2 2 3 + 2 10} i, x = - \frac{3 + 2 10}{2 2} - \frac{31}{2 2 3 + 2 10} i

求解步骤

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

整理后得

- 2 x^{4} + 3 x^{2} - 5 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

- 2 u^{2} + 3 u - 5 = 0

解

- 2 u^{2} + 3 u - 5 = 0 : u = \frac{3}{4} - i \frac{31}{4}, u = \frac{3}{4} + i \frac{31}{4}

u = \frac{3}{4} - i \frac{31}{4}, u = \frac{3}{4} + i \frac{31}{4}

代回

u = x^{2}

，求解

x

解

x^{2} = \frac{3}{4} - i \frac{31}{4} : x = \frac{3 + 2 10}{2 2} - \frac{31}{2 2 3 + 2 10} i, x = - \frac{3 + 2 10}{2 2} + \frac{31}{2 2 3 + 2 10} i

解

x^{2} = \frac{3}{4} + i \frac{31}{4} : x = \frac{3 + 2 10}{2 2} + \frac{31}{2 2 3 + 2 10} i, x = - \frac{3 + 2 10}{2 2} - \frac{31}{2 2 3 + 2 10} i

解为

x = \frac{3 + 2 10}{2 2} - \frac{31}{2 2 3 + 2 10} i, x = - \frac{3 + 2 10}{2 2} + \frac{31}{2 2 3 + 2 10} i, x = \frac{3 + 2 10}{2 2} + \frac{31}{2 2 3 + 2 10} i, x = - \frac{3 + 2 10}{2 2} - \frac{31}{2 2 3 + 2 10} i

作图

流行的例子

x^{5} + x - 2 = 0

x^3-4x^2-x+10=0

x^{3} - 4 x^{2} - x + 10 = 0

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

e a^{4} = 5, a^{1} = 20

1x^3-1x^2-2x+2=0

1 x^{3} - 1 x^{2} - 2 x + 2 = 0