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人気のある代数 >

288=24x^{12}

解

288 = 24 x^{12}

解

x = 612, x = - 612, x = 612 i, x = - 612 i, x = 1.06527 \dots + \frac{2.28942 \dots - 0.75654 \dots}{2} i, x = - 1.06527 \dots - \frac{2.28942 \dots - 0.75654 \dots}{2} i, x = - 0.61503 \dots + \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = 0.61503 \dots - \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = 0.61503 \dots + \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = - 0.61503 \dots - \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = - 1.06527 \dots + \frac{2.28942 \dots - 0.75654 \dots}{2} i, x = 1.06527 \dots - \frac{2.28942 \dots - 0.75654 \dots}{2} i

解答ステップ

288 = 24 x^{12}

辺を交換する

24 x^{12} = 288

以下で両辺を割る

24

x^{12} = 12

equationを

u = x^{2}

と以下で書き換える:

u^{6} = x^{12}

u^{6} = 12

解く

u^{6} = 12 : u = 312, u = - 312, u = \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} + 1.31037 \dots i, u = - \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} - 1.31037 \dots i, u = - \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} + 1.31037 \dots i, u = \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} - 1.31037 \dots i

u = 312, u = - 312, u = \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} + 1.31037 \dots i, u = - \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} - 1.31037 \dots i, u = - \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} + 1.31037 \dots i, u = \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} - 1.31037 \dots i

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = 312 : x = 612, x = - 612

解く

x^{2} = - 312 : x = 612 i, x = - 612 i

解く

x^{2} = \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} + 1.31037 \dots i : x = 1.06527 \dots + \frac{2.28942 \dots - 0.75654 \dots}{2} i, x = - 1.06527 \dots - \frac{2.28942 \dots - 0.75654 \dots}{2} i

解く

x^{2} = - \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} - 1.31037 \dots i : x = - 0.61503 \dots + \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = 0.61503 \dots - \frac{0.75654 \dots + 2.28942 \dots}{2} i

解く

x^{2} = - \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} + 1.31037 \dots i : x = 0.61503 \dots + \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = - 0.61503 \dots - \frac{0.75654 \dots + 2.28942 \dots}{2} i

解く

x^{2} = \frac{3 ^{\frac{5}{6}}}{2.62074 \dots 3 2} - 1.31037 \dots i : x = - 1.06527 \dots + \frac{2.28942 \dots - 0.75654 \dots}{2} i, x = 1.06527 \dots - \frac{2.28942 \dots - 0.75654 \dots}{2} i

解答は

x = 612, x = - 612, x = 612 i, x = - 612 i, x = 1.06527 \dots + \frac{2.28942 \dots - 0.75654 \dots}{2} i, x = - 1.06527 \dots - \frac{2.28942 \dots - 0.75654 \dots}{2} i, x = - 0.61503 \dots + \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = 0.61503 \dots - \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = 0.61503 \dots + \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = - 0.61503 \dots - \frac{0.75654 \dots + 2.28942 \dots}{2} i, x = - 1.06527 \dots + \frac{2.28942 \dots - 0.75654 \dots}{2} i, x = 1.06527 \dots - \frac{2.28942 \dots - 0.75654 \dots}{2} i

グラフ

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