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受欢迎的代数 >

y^8+5=-3

解答

y^{8} + 5 = - 3

解答

y = \frac{1}{2 ^{\frac{1}{8}} 2 - 2 ^{\frac{1}{2}}} + \frac{2 - 2 ^{\frac{1}{2}}}{2 ^{\frac{5}{8}}} i, y = - \frac{1}{2 ^{\frac{1}{8}} 2 - 2 ^{\frac{1}{2}}} - \frac{2 - 2 ^{\frac{1}{2}}}{2 ^{\frac{5}{8}}} i, y = - \frac{1}{2 ^{\frac{3}{4}} + 2 4 2} + \frac{2 ^{\frac{3}{4}} + 2 4 2}{2 ^{\frac{3}{4}}} i, y = \frac{1}{2 ^{\frac{3}{4}} + 2 4 2} - \frac{2 ^{\frac{3}{4}} + 2 4 2}{2 ^{\frac{3}{4}}} i, y = \frac{1}{2 ^{\frac{3}{4}} + 2 4 2} + \frac{2 ^{\frac{3}{4}} + 2 4 2}{2 ^{\frac{3}{4}}} i, y = - \frac{1}{2 ^{\frac{3}{4}} + 2 4 2} - \frac{2 ^{\frac{3}{4}} + 2 4 2}{2 ^{\frac{3}{4}}} i, y = - \frac{1}{2 ^{\frac{1}{8}} 2 - 2 ^{\frac{1}{2}}} + \frac{2 - 2 ^{\frac{1}{2}}}{2 ^{\frac{5}{8}}} i, y = \frac{1}{2 ^{\frac{1}{8}} 2 - 2 ^{\frac{1}{2}}} - \frac{2 - 2 ^{\frac{1}{2}}}{2 ^{\frac{5}{8}}} i

求解步骤

y^{8} + 5 = - 3

将

5

到右边

y^{8} = - 8

用

u = y^{2}

和

u^{4} = y^{8}

改写方程式

u^{4} = - 8

解

u^{4} = - 8 : u = 42 + 42 i, u = - 42 - 42 i, u = - 42 + 42 i, u = 42 - 42 i

u = 42 + 42 i, u = - 42 - 42 i, u = - 42 + 42 i, u = 42 - 42 i

代回

u = y^{2}

，求解

y

解

y^{2} = 42 + 42 i : y = \frac{1}{2 ^{\frac{1}{8}} 2 - 2 ^{\frac{1}{2}}} + \frac{2 - 2 ^{\frac{1}{2}}}{2 ^{\frac{5}{8}}} i, y = - \frac{1}{2 ^{\frac{1}{8}} 2 - 2 ^{\frac{1}{2}}} - \frac{2 - 2 ^{\frac{1}{2}}}{2 ^{\frac{5}{8}}} i

解

y^{2} = - 42 - 42 i : y = - \frac{1}{2 ^{\frac{3}{4}} + 2 4 2} + \frac{2 ^{\frac{3}{4}} + 2 4 2}{2 ^{\frac{3}{4}}} i, y = \frac{1}{2 ^{\frac{3}{4}} + 2 4 2} - \frac{2 ^{\frac{3}{4}} + 2 4 2}{2 ^{\frac{3}{4}}} i

解

y^{2} = - 42 + 42 i : y = \frac{1}{2 ^{\frac{3}{4}} + 2 4 2} + \frac{2 ^{\frac{3}{4}} + 2 4 2}{2 ^{\frac{3}{4}}} i, y = - \frac{1}{2 ^{\frac{3}{4}} + 2 4 2} - \frac{2 ^{\frac{3}{4}} + 2 4 2}{2 ^{\frac{3}{4}}} i

解

y^{2} = 42 - 42 i : y = - \frac{1}{2 ^{\frac{1}{8}} 2 - 2 ^{\frac{1}{2}}} + \frac{2 - 2 ^{\frac{1}{2}}}{2 ^{\frac{5}{8}}} i, y = \frac{1}{2 ^{\frac{1}{8}} 2 - 2 ^{\frac{1}{2}}} - \frac{2 - 2 ^{\frac{1}{2}}}{2 ^{\frac{5}{8}}} i

解为

y = \frac{1}{2 ^{\frac{1}{8}} 2 - 2 ^{\frac{1}{2}}} + \frac{2 - 2 ^{\frac{1}{2}}}{2 ^{\frac{5}{8}}} i, y = - \frac{1}{2 ^{\frac{1}{8}} 2 - 2 ^{\frac{1}{2}}} - \frac{2 - 2 ^{\frac{1}{2}}}{2 ^{\frac{5}{8}}} i, y = - \frac{1}{2 ^{\frac{3}{4}} + 2 4 2} + \frac{2 ^{\frac{3}{4}} + 2 4 2}{2 ^{\frac{3}{4}}} i, y = \frac{1}{2 ^{\frac{3}{4}} + 2 4 2} - \frac{2 ^{\frac{3}{4}} + 2 4 2}{2 ^{\frac{3}{4}}} i, y = \frac{1}{2 ^{\frac{3}{4}} + 2 4 2} + \frac{2 ^{\frac{3}{4}} + 2 4 2}{2 ^{\frac{3}{4}}} i, y = - \frac{1}{2 ^{\frac{3}{4}} + 2 4 2} - \frac{2 ^{\frac{3}{4}} + 2 4 2}{2 ^{\frac{3}{4}}} i, y = - \frac{1}{2 ^{\frac{1}{8}} 2 - 2 ^{\frac{1}{2}}} + \frac{2 - 2 ^{\frac{1}{2}}}{2 ^{\frac{5}{8}}} i, y = \frac{1}{2 ^{\frac{1}{8}} 2 - 2 ^{\frac{1}{2}}} - \frac{2 - 2 ^{\frac{1}{2}}}{2 ^{\frac{5}{8}}} i

作图

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