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 >

m^4+m^2+16=0

解答

m^{4} + m^{2} + 16 = 0

解答

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

求解步骤

m^{4} + m^{2} + 16 = 0

用

u = m^{2}

和

u^{2} = m^{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 = m^{2}

，求解

m

解

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

解

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

解为

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

作图

流行的例子

785 = 5 x^{3}

x^3+4x^2+10x+15=0

x^{3} + 4 x^{2} + 10 x + 15 = 0

(x^2+2)(x^2-1)=0

(x^{2} + 2) (x^{2} - 1) = 0

x^3+12x^2-60x+64=0

x^{3} + 12 x^{2} - 60 x + 64 = 0

x^{6} - 12 x^{3} + 27 = 0