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人気のある代数 >

x^8+8x^4=9

解

x^{8} + 8 x^{4} = 9

解

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

解答ステップ

x^{8} + 8 x^{4} = 9

9

を左側に移動します

x^{8} + 8 x^{4} - 9 = 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} + 8 u^{2} - 9 = 0

解く

u^{4} + 8 u^{2} - 9 = 0 : u = 1, u = - 1, u = 3 i, u = - 3 i

u = 1, u = - 1, u = 3 i, u = - 3 i

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} = - 1 : x = i, x = - i

解く

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

解く

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

解答は

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

グラフ

人気の例

w^{3} = 1000

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