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人気のある代数 >

x^4-2x^2+2=0

解

x^{4} - 2 x^{2} + 2 = 0

解

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

解答ステップ

x^{4} - 2 x^{2} + 2 = 0

equationを

u = x^{2}

と以下で書き換える:

u^{2} = x^{4}

u^{2} - 2 u + 2 = 0

解く

u^{2} - 2 u + 2 = 0 : u = 1 + i, u = 1 - i

u = 1 + i, u = 1 - i

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

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

解く

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

解答は

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

グラフ

人気の例

8 y^{3} - 125 = 0

(x + 6)^{4} = 0

4 x^{3} - 6 x^{2} + 1 = 0

x^{4} - 5 x = 0

20u^4-13u^2+2=0

20 u^{4} - 13 u^{2} + 2 = 0