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人気のある代数 >

x^8+16=17x^4

解

x^{8} + 16 = 17 x^{4}

解

x = 2, x = - 2, x = 2 i, x = - 2 i, x = 1, x = - 1, x = i, x = - i

解答ステップ

x^{8} + 16 = 17 x^{4}

17 x^{4}

を左側に移動します

x^{8} + 16 - 17 x^{4} = 0

標準的な形式で書く

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{8} - 17 x^{4} + 16 = 0

equationを

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

と以下で書き換える:

u^{4} = x^{8}

u^{4} - 17 u^{2} + 16 = 0

解く

u^{4} - 17 u^{2} + 16 = 0 : u = 4, u = - 4, u = 1, u = - 1

u = 4, u = - 4, u = 1, u = - 1

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = 4 : x = 2, x = - 2

解く

x^{2} = - 4 : x = 2 i, x = - 2 i

解く

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

解く

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

解答は

x = 2, x = - 2, x = 2 i, x = - 2 i, x = 1, x = - 1, x = i, x = - i

グラフ

人気の例

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y^{3} + 5 y^{2} - 36 y - 180 = 0

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