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受欢迎的代数 >

2x^4+5=0

解答

2 x^{4} + 5 = 0

解答

x = 4 \frac{5}{8} + \frac{4 5}{2 ^{\frac{3}{4}}} i, x = - 4 \frac{5}{8} - \frac{4 5}{2 ^{\frac{3}{4}}} i, x = 4 \frac{5}{8} - \frac{4 5}{2 ^{\frac{3}{4}}} i, x = - 4 \frac{5}{8} + \frac{4 5}{2 ^{\frac{3}{4}}} i

求解步骤

2 x^{4} + 5 = 0

将

5

到右边

2 x^{4} = - 5

两边除以

2

x^{4} = - \frac{5}{2}

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

u^{2} = - \frac{5}{2}

解

u^{2} = - \frac{5}{2} : u = \frac{5}{2} i, u = - \frac{5}{2} i

u = \frac{5}{2} i, u = - \frac{5}{2} i

代回

u = x^{2}

，求解

x

解

x^{2} = \frac{5}{2} i : x = 4 \frac{5}{8} + \frac{4 5}{2 ^{\frac{3}{4}}} i, x = - 4 \frac{5}{8} - \frac{4 5}{2 ^{\frac{3}{4}}} i

解

x^{2} = - \frac{5}{2} i : x = 4 \frac{5}{8} - \frac{4 5}{2 ^{\frac{3}{4}}} i, x = - 4 \frac{5}{8} + \frac{4 5}{2 ^{\frac{3}{4}}} i

解为

x = 4 \frac{5}{8} + \frac{4 5}{2 ^{\frac{3}{4}}} i, x = - 4 \frac{5}{8} - \frac{4 5}{2 ^{\frac{3}{4}}} i, x = 4 \frac{5}{8} - \frac{4 5}{2 ^{\frac{3}{4}}} i, x = - 4 \frac{5}{8} + \frac{4 5}{2 ^{\frac{3}{4}}} i

作图

流行的例子

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