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受欢迎的代数 >

2x^8-3+5=15

解答

2 x^{8} - 3 + 5 = 15

解答

x = 4 \frac{13}{2}, x = - 4 \frac{13}{2}, x = - 4 \frac{13}{2}, x = - - 4 \frac{13}{2}, x = 8 \frac{13}{32} + i 8 \frac{13}{32}, x = - 8 \frac{13}{32} - i 8 \frac{13}{32}, x = 8 \frac{13}{32} - i 8 \frac{13}{32}, x = - 8 \frac{13}{32} + i 8 \frac{13}{32}

求解步骤

2 x^{8} - 3 + 5 = 15

将

3

到右边

2 x^{8} + 5 = 18

将

5

到右边

2 x^{8} = 13

两边除以

2

x^{8} = \frac{13}{2}

用

u = x^{2}

和

u^{4} = x^{8}

改写方程式

u^{4} = \frac{13}{2}

解

u^{4} = \frac{13}{2} : u = \frac{13}{2}, u = - \frac{13}{2}, u = - \frac{13}{2}, u = - - \frac{13}{2}

u = \frac{13}{2}, u = - \frac{13}{2}, u = - \frac{13}{2}, u = - - \frac{13}{2}

代回

u = x^{2}

，求解

x

解

x^{2} = \frac{13}{2} : x = 4 \frac{13}{2}, x = - 4 \frac{13}{2}

解

x^{2} = - \frac{13}{2} : x = - 4 \frac{13}{2}, x = - - 4 \frac{13}{2}

解

x^{2} = - \frac{13}{2} : x = 8 \frac{13}{32} + i 8 \frac{13}{32}, x = - 8 \frac{13}{32} - i 8 \frac{13}{32}

解

x^{2} = - - \frac{13}{2} : x = 8 \frac{13}{32} - i 8 \frac{13}{32}, x = - 8 \frac{13}{32} + i 8 \frac{13}{32}

解为

x = 4 \frac{13}{2}, x = - 4 \frac{13}{2}, x = - 4 \frac{13}{2}, x = - - 4 \frac{13}{2}, x = 8 \frac{13}{32} + i 8 \frac{13}{32}, x = - 8 \frac{13}{32} - i 8 \frac{13}{32}, x = 8 \frac{13}{32} - i 8 \frac{13}{32}, x = - 8 \frac{13}{32} + i 8 \frac{13}{32}

作图

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