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人気のある代数 >

x^8=-1

解

x^{8} = - 1

解

x = \frac{1}{2 ^{\frac{3}{4}} 2 - 1} + \frac{2 - 1}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 2 - 1} - \frac{2 - 1}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} + \frac{1 + 2}{4 2 ^{3}} i, x = \frac{1}{2 ^{\frac{3}{4}} 1 + 2} - \frac{1 + 2}{4 2 ^{3}} i, x = \frac{1}{2 ^{\frac{3}{4}} 1 + 2} + \frac{1 + 2}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} - \frac{1 + 2}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 2 - 1} + \frac{2 - 1}{4 2 ^{3}} i, x = \frac{1}{2 ^{\frac{3}{4}} 2 - 1} - \frac{2 - 1}{4 2 ^{3}} i

解答ステップ

x^{8} = - 1

equationを

u = x^{2}

と以下で書き換える:

u^{4} = x^{8}

u^{4} = - 1

解く

u^{4} = - 1 : u = \frac{1}{2} + \frac{1}{2} i, u = - \frac{1}{2} - \frac{1}{2} i, u = - \frac{1}{2} + \frac{1}{2} i, u = \frac{1}{2} - \frac{1}{2} i

u = \frac{1}{2} + \frac{1}{2} i, u = - \frac{1}{2} - \frac{1}{2} i, u = - \frac{1}{2} + \frac{1}{2} i, u = \frac{1}{2} - \frac{1}{2} i

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = \frac{1}{2} + \frac{1}{2} i : x = \frac{1}{2 ^{\frac{3}{4}} 2 - 1} + \frac{2 - 1}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 2 - 1} - \frac{2 - 1}{4 2 ^{3}} i

解く

x^{2} = - \frac{1}{2} - \frac{1}{2} i : x = - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} + \frac{1 + 2}{4 2 ^{3}} i, x = \frac{1}{2 ^{\frac{3}{4}} 1 + 2} - \frac{1 + 2}{4 2 ^{3}} i

解く

x^{2} = - \frac{1}{2} + \frac{1}{2} i : x = \frac{1}{2 ^{\frac{3}{4}} 1 + 2} + \frac{1 + 2}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} - \frac{1 + 2}{4 2 ^{3}} i

解く

x^{2} = \frac{1}{2} - \frac{1}{2} i : x = - \frac{1}{2 ^{\frac{3}{4}} 2 - 1} + \frac{2 - 1}{4 2 ^{3}} i, x = \frac{1}{2 ^{\frac{3}{4}} 2 - 1} - \frac{2 - 1}{4 2 ^{3}} i

解答は

x = \frac{1}{2 ^{\frac{3}{4}} 2 - 1} + \frac{2 - 1}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 2 - 1} - \frac{2 - 1}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} + \frac{1 + 2}{4 2 ^{3}} i, x = \frac{1}{2 ^{\frac{3}{4}} 1 + 2} - \frac{1 + 2}{4 2 ^{3}} i, x = \frac{1}{2 ^{\frac{3}{4}} 1 + 2} + \frac{1 + 2}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} - \frac{1 + 2}{4 2 ^{3}} i, x = - \frac{1}{2 ^{\frac{3}{4}} 2 - 1} + \frac{2 - 1}{4 2 ^{3}} i, x = \frac{1}{2 ^{\frac{3}{4}} 2 - 1} - \frac{2 - 1}{4 2 ^{3}} i

グラフ

人気の例

x^{8} = 32

-x^3+8x^2-4x-48=0

- x^{3} + 8 x^{2} - 4 x - 48 = 0

12 = + x x^{3}

m^{3} = 5

x^3-4x^2-53x+168=0

x^{3} - 4 x^{2} - 53 x + 168 = 0