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受欢迎的代数 >

x^4+2x^2+4=0

解答

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

解答

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

求解步骤

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

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

u^{2} + 2 u + 4 = 0

解

u^{2} + 2 u + 4 = 0 : u = - 1 + 3 i, u = - 1 - 3 i

u = - 1 + 3 i, u = - 1 - 3 i

代回

u = x^{2}

，求解

x

解

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

解

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

解为

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

作图

流行的例子

5y^3+17y-12=9y^2-9y

5 y^{3} + 17 y - 12 = 9 y^{2} - 9 y

4x+3=x^3+3x^2-9x-12

4 x + 3 = x^{3} + 3 x^{2} - 9 x - 12

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

5x^3+23x^2+20x-12=0

5 x^{3} + 23 x^{2} + 20 x - 12 = 0

x^{3} - x - 3360 = 0