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人気のある代数 >

x^6-7x^3-8=0

解

x^{6} - 7 x^{3} - 8 = 0

解

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

解答ステップ

x^{6} - 7 x^{3} - 8 = 0

equationを

u = x^{3}

と以下で書き換える:

u^{2} = x^{6}

u^{2} - 7 u - 8 = 0

解く

u^{2} - 7 u - 8 = 0 : u = 8, u = - 1

u = 8, u = - 1

再び

u = x^{3}

に置き換えて以下を解く:

x

解く

x^{3} = 8 : x = 2, x = - 1 + 3 i, x = - 1 - 3 i

解く

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

解答は

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

グラフ

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