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人気のある代数 >

x^6+11x^4-81x^2+69=0

解

x^{6} + 11 x^{4} - 81 x^{2} + 69 = 0

解

x = 1, x = - 1, x = - 6 + 105, x = - - 6 + 105, x = 6 + 105 i, x = - 6 + 105 i

解答ステップ

x^{6} + 11 x^{4} - 81 x^{2} + 69 = 0

equationを

u = x^{2}, u^{2} = x^{4}

と以下で書き換える:

u^{3} = x^{6}

u^{3} + 11 u^{2} - 81 u + 69 = 0

解く

u^{3} + 11 u^{2} - 81 u + 69 = 0 : u = 1, u = - 6 + 105, u = - 6 - 105

u = 1, u = - 6 + 105, u = - 6 - 105

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = 1 : x = 1, x = - 1

解く

x^{2} = - 6 + 105 : x = - 6 + 105, x = - - 6 + 105

解く

x^{2} = - 6 - 105 : x = 6 + 105 i, x = - 6 + 105 i

解答は

x = 1, x = - 1, x = - 6 + 105, x = - - 6 + 105, x = 6 + 105 i, x = - 6 + 105 i

グラフ

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