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人気のある代数 >

x^4+1=0

解

x^{4} + 1 = 0

解

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

解答ステップ

x^{4} + 1 = 0

1

を右側に移動します

x^{4} = - 1

equationを

u = x^{2}

と以下で書き換える:

u^{2} = x^{4}

u^{2} = - 1

解く

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

u = i, u = - i

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

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

解く

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

解答は

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

グラフ

人気の例

x^{3} - x = x^{2} + 2

x^4-4x^3+4x^2-10=0

x^{4} - 4 x^{3} + 4 x^{2} - 10 = 0

3 x^{4} - 8 x^{2} + 4 = 0

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

a=(x^3+1)(x^6-x^3+1)

a = (x^{3} + 1) (x^{6} - x^{3} + 1)