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人気のある代数 >

x^4-x^2+1=0

解

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

解

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

解答ステップ

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

equationを

u = x^{2}

と以下で書き換える:

u^{2} = x^{4}

u^{2} - u + 1 = 0

解く

u^{2} - u + 1 = 0 : u = \frac{1}{2} + i \frac{3}{2}, u = \frac{1}{2} - i \frac{3}{2}

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

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

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

解く

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

解答は

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

グラフ

人気の例

x^{3} + x^{2} + 4 x + 4 = 0

8 x^{4} = x

x^{5} + (2 - x)^{5} = 82

x^{3} - 5 x^{2} + 6 x = 0

(x^{2} + 1)^{3} = 0