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受欢迎的代数 >

(x^{12}-1)8=x^{84}-1

解答

(x^{12} - 1) 8 = x^{84} - 1

解答

x = 1, x = - 1, x = 6 \frac{5.22107 E 13}{5.0 E 13}, x = - 6 \frac{5.22107 E 13}{5.0 E 13}

+1

十进制

x = 1, x = - 1, x = 1.00361 \dots, x = - 1.00361 \dots

求解步骤

(x^{12} - 1) \cdot 8 = x^{84} - 1

展开

(x^{12} - 1) \cdot 8 : 8 x^{12} - 8

8 x^{12} - 8 = x^{84} - 1

交换两边

x^{84} - 1 = 8 x^{12} - 8

将

8

para o lado esquerdo

x^{84} + 7 = 8 x^{12}

将

8 x^{12}

para o lado esquerdo

x^{84} + 7 - 8 x^{12} = 0

改写成标准形式

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{84} - 8 x^{12} + 7 = 0

用

u = x^{2}, u^{6} = x^{12}

和

u^{42} = x^{84}

改写方程式

u^{42} - 8 u^{6} + 7 = 0

解

u^{42} - 8 u^{6} + 7 = 0 : u = 1, u = - 1, u = 3 \frac{5.22107 E 13}{5.0 E 13}, u = - 3 \frac{5.22107 E 13}{5.0 E 13}

u = 1, u = - 1, u = 3 \frac{5.22107 E 13}{5.0 E 13}, u = - 3 \frac{5.22107 E 13}{5.0 E 13}

代回

u = x^{2}

，求解

x

解

x^{2} = 1 : x = 1, x = - 1

解

x^{2} = - 1 : x \in R

无解

解

x^{2} = 3 \frac{5.22107 E 13}{5.0 E 13} : x = 6 \frac{5.22107 E 13}{5.0 E 13}, x = - 6 \frac{5.22107 E 13}{5.0 E 13}

解

x^{2} = - 3 \frac{5.22107 E 13}{5.0 E 13} : x \in R

无解

解为

x = 1, x = - 1, x = 6 \frac{5.22107 E 13}{5.0 E 13}, x = - 6 \frac{5.22107 E 13}{5.0 E 13}

作图

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