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 >

2z^6-15z^3-27=0

解答

2 z^{6} - 15 z^{3} - 27 = 0

解答

z = 39, z = - 39 \frac{1}{2} + 39 \frac{3}{2} i, z = - 39 \frac{1}{2} - 39 \frac{3}{2} i, z = - 3 \frac{3}{2}, z = \frac{3 3}{2 3 2} - \frac{6 3 ^{5}}{2 3 2} i, z = \frac{3 3}{2 3 2} + \frac{6 3 ^{5}}{2 3 2} i

求解步骤

2 z^{6} - 15 z^{3} - 27 = 0

用

u = z^{3}

和

u^{2} = z^{6}

改写方程式

2 u^{2} - 15 u - 27 = 0

解

2 u^{2} - 15 u - 27 = 0 : u = 9, u = - \frac{3}{2}

u = 9, u = - \frac{3}{2}

代回

u = z^{3}

，求解

z

解

z^{3} = 9 : z = 39, z = - 39 \frac{1}{2} + 39 \frac{3}{2} i, z = - 39 \frac{1}{2} - 39 \frac{3}{2} i

解

z^{3} = - \frac{3}{2} : z = - 3 \frac{3}{2}, z = \frac{3 3}{2 3 2} - \frac{6 3 ^{5}}{2 3 2} i, z = \frac{3 3}{2 3 2} + \frac{6 3 ^{5}}{2 3 2} i

解为

z = 39, z = - 39 \frac{1}{2} + 39 \frac{3}{2} i, z = - 39 \frac{1}{2} - 39 \frac{3}{2} i, z = - 3 \frac{3}{2}, z = \frac{3 3}{2 3 2} - \frac{6 3 ^{5}}{2 3 2} i, z = \frac{3 3}{2 3 2} + \frac{6 3 ^{5}}{2 3 2} i

作图

流行的例子

(x^2+7x+49)(x-7)=218

(x^{2} + 7 x + 49) (x - 7) = 218

4x^3-2x^2+3x-1=0

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

x^{3} + 3 x^{2} - 58 = 0

(x+2)^2=x(x^2-10x+25)

(x + 2)^{2} = x (x^{2} - 10 x + 25)

w+w^2-w^3+w^4=5

w + w^{2} - w^{3} + w^{4} = 5