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人気のある代数 >

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

解

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

解

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

十進法表記

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

解答ステップ

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

拡張

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

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

辺を交換する

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

8

を左側に移動します

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

8 x^{12}

を左側に移動します

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

標準的な形式で書く

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

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

equationを

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

と以下で書き換える:

u^{42} = x^{84}

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

解く

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}

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

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

解く

x^{2} = - 1 :

以下の解はない:

x \in R

解く

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}

解く

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

以下の解はない:

x \in R

解答は

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}

グラフ

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