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人気のある代数 >

x^{12}=832

解

x^{12} = 832

解

x = 21213, x = - 21213, x = 21213 i, x = - 21213 i, x = - 0.87561 \dots + \frac{1.53340 \dots + 9.40533 \dots}{2} i, x = 0.87561 \dots - \frac{1.53340 \dots + 9.40533 \dots}{2} i, x = 1.51661 \dots + \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = - 1.51661 \dots - \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = - 1.51661 \dots + \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = 1.51661 \dots - \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = 0.87561 \dots + \frac{1.53340 \dots + 9.40533 \dots}{2} i, x = - 0.87561 \dots - \frac{1.53340 \dots + 9.40533 \dots}{2} i

解答ステップ

x^{12} = 832

equationを

u = x^{2}

と以下で書き換える:

u^{6} = x^{12}

u^{6} = 832

解く

u^{6} = 832 : u = 2613, u = - 2613, u = - 1.53340 \dots - 2.65593 \dots i, u = 1.53340 \dots + 2.65593 \dots i, u = 1.53340 \dots - 2.65593 \dots i, u = - 1.53340 \dots + 2.65593 \dots i

u = 2613, u = - 2613, u = - 1.53340 \dots - 2.65593 \dots i, u = 1.53340 \dots + 2.65593 \dots i, u = 1.53340 \dots - 2.65593 \dots i, u = - 1.53340 \dots + 2.65593 \dots i

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = 2613 : x = 21213, x = - 21213

解く

x^{2} = - 2613 : x = 21213 i, x = - 21213 i

解く

x^{2} = - 1.53340 \dots - 2.65593 \dots i : x = - 0.87561 \dots + \frac{1.53340 \dots + 9.40533 \dots}{2} i, x = 0.87561 \dots - \frac{1.53340 \dots + 9.40533 \dots}{2} i

解く

x^{2} = 1.53340 \dots + 2.65593 \dots i : x = 1.51661 \dots + \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = - 1.51661 \dots - \frac{9.40533 \dots - 1.53340 \dots}{2} i

解く

x^{2} = 1.53340 \dots - 2.65593 \dots i : x = - 1.51661 \dots + \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = 1.51661 \dots - \frac{9.40533 \dots - 1.53340 \dots}{2} i

解く

x^{2} = - 1.53340 \dots + 2.65593 \dots i : x = 0.87561 \dots + \frac{1.53340 \dots + 9.40533 \dots}{2} i, x = - 0.87561 \dots - \frac{1.53340 \dots + 9.40533 \dots}{2} i

解答は

x = 21213, x = - 21213, x = 21213 i, x = - 21213 i, x = - 0.87561 \dots + \frac{1.53340 \dots + 9.40533 \dots}{2} i, x = 0.87561 \dots - \frac{1.53340 \dots + 9.40533 \dots}{2} i, x = 1.51661 \dots + \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = - 1.51661 \dots - \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = - 1.51661 \dots + \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = 1.51661 \dots - \frac{9.40533 \dots - 1.53340 \dots}{2} i, x = 0.87561 \dots + \frac{1.53340 \dots + 9.40533 \dots}{2} i, x = - 0.87561 \dots - \frac{1.53340 \dots + 9.40533 \dots}{2} i

グラフ

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