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人気のある代数 >

x^{12}-1=4

解

x^{12} - 1 = 4

解

x = 65, x = - 65, x = 65 i, x = - 65 i, x = 0.99032 \dots + \frac{1.70997 \dots - 0.65383 \dots}{2} i, x = - 0.99032 \dots - \frac{1.70997 \dots - 0.65383 \dots}{2} i, x = - 0.57176 \dots + \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = 0.57176 \dots - \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = 0.57176 \dots + \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = - 0.57176 \dots - \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = - 0.99032 \dots + \frac{1.70997 \dots - 0.65383 \dots}{2} i, x = 0.99032 \dots - \frac{1.70997 \dots - 0.65383 \dots}{2} i

解答ステップ

x^{12} - 1 = 4

1

を右側に移動します

x^{12} = 5

equationを

u = x^{2}

と以下で書き換える:

u^{6} = x^{12}

u^{6} = 5

解く

u^{6} = 5 : u = 35, u = - 35, u = 0.65383 \dots + 1.13246 \dots i, u = - 0.65383 \dots - 1.13246 \dots i, u = - 0.65383 \dots + 1.13246 \dots i, u = 0.65383 \dots - 1.13246 \dots i

u = 35, u = - 35, u = 0.65383 \dots + 1.13246 \dots i, u = - 0.65383 \dots - 1.13246 \dots i, u = - 0.65383 \dots + 1.13246 \dots i, u = 0.65383 \dots - 1.13246 \dots i

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = 35 : x = 65, x = - 65

解く

x^{2} = - 35 : x = 65 i, x = - 65 i

解く

x^{2} = 0.65383 \dots + 1.13246 \dots i : x = 0.99032 \dots + \frac{1.70997 \dots - 0.65383 \dots}{2} i, x = - 0.99032 \dots - \frac{1.70997 \dots - 0.65383 \dots}{2} i

解く

x^{2} = - 0.65383 \dots - 1.13246 \dots i : x = - 0.57176 \dots + \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = 0.57176 \dots - \frac{0.65383 \dots + 1.70997 \dots}{2} i

解く

x^{2} = - 0.65383 \dots + 1.13246 \dots i : x = 0.57176 \dots + \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = - 0.57176 \dots - \frac{0.65383 \dots + 1.70997 \dots}{2} i

解く

x^{2} = 0.65383 \dots - 1.13246 \dots i : x = - 0.99032 \dots + \frac{1.70997 \dots - 0.65383 \dots}{2} i, x = 0.99032 \dots - \frac{1.70997 \dots - 0.65383 \dots}{2} i

解答は

x = 65, x = - 65, x = 65 i, x = - 65 i, x = 0.99032 \dots + \frac{1.70997 \dots - 0.65383 \dots}{2} i, x = - 0.99032 \dots - \frac{1.70997 \dots - 0.65383 \dots}{2} i, x = - 0.57176 \dots + \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = 0.57176 \dots - \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = 0.57176 \dots + \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = - 0.57176 \dots - \frac{0.65383 \dots + 1.70997 \dots}{2} i, x = - 0.99032 \dots + \frac{1.70997 \dots - 0.65383 \dots}{2} i, x = 0.99032 \dots - \frac{1.70997 \dots - 0.65383 \dots}{2} i

グラフ

人気の例

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