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 >

x^6+3x^3-5=0

解答

x^{6} + 3 x^{3} - 5 = 0

解答

x = 3 \frac{- 3 + 29}{2}, x = - 3 \frac{- 3 + 29}{2} \frac{1}{2} + 3 \frac{- 3 + 29}{2} \frac{3}{2} i, x = - 3 \frac{- 3 + 29}{2} \frac{1}{2} - 3 \frac{- 3 + 29}{2} \frac{3}{2} i, x = 3 \frac{- 3 - 29}{2}, x = - 3 \frac{- 3 - 29}{2} \frac{1}{2} + 3 \frac{- 3 - 29}{2} \frac{3}{2} i, x = - 3 \frac{- 3 - 29}{2} \frac{1}{2} - 3 \frac{- 3 - 29}{2} \frac{3}{2} i

求解步骤

x^{6} + 3 x^{3} - 5 = 0

用

u = x^{3}

和

u^{2} = x^{6}

改写方程式

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

解

u^{2} + 3 u - 5 = 0 : u = \frac{- 3 + 29}{2}, u = \frac{- 3 - 29}{2}

u = \frac{- 3 + 29}{2}, u = \frac{- 3 - 29}{2}

代回

u = x^{3}

，求解

x

解

x^{3} = \frac{- 3 + 29}{2} : x = 3 \frac{- 3 + 29}{2}, x = - 3 \frac{- 3 + 29}{2} \frac{1}{2} + 3 \frac{- 3 + 29}{2} \frac{3}{2} i, x = - 3 \frac{- 3 + 29}{2} \frac{1}{2} - 3 \frac{- 3 + 29}{2} \frac{3}{2} i

解

x^{3} = \frac{- 3 - 29}{2} : x = 3 \frac{- 3 - 29}{2}, x = - 3 \frac{- 3 - 29}{2} \frac{1}{2} + 3 \frac{- 3 - 29}{2} \frac{3}{2} i, x = - 3 \frac{- 3 - 29}{2} \frac{1}{2} - 3 \frac{- 3 - 29}{2} \frac{3}{2} i

解为

x = 3 \frac{- 3 + 29}{2}, x = - 3 \frac{- 3 + 29}{2} \frac{1}{2} + 3 \frac{- 3 + 29}{2} \frac{3}{2} i, x = - 3 \frac{- 3 + 29}{2} \frac{1}{2} - 3 \frac{- 3 + 29}{2} \frac{3}{2} i, x = 3 \frac{- 3 - 29}{2}, x = - 3 \frac{- 3 - 29}{2} \frac{1}{2} + 3 \frac{- 3 - 29}{2} \frac{3}{2} i, x = - 3 \frac{- 3 - 29}{2} \frac{1}{2} - 3 \frac{- 3 - 29}{2} \frac{3}{2} i

作图

流行的例子

2y^4-9y^3+14y^2+6y-63=0

2 y^{4} - 9 y^{3} + 14 y^{2} + 6 y - 63 = 0

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

5 z^{3} + 22 z^{2} = 15 z

solvefor x,x^3-4y^2+3=0

so l v e f or x, x^{3} - 4 y^{2} + 3 = 0

solvefor x,x^6+4x^3+16=0

so l v e f or x, x^{6} + 4 x^{3} + 16 = 0