ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

4 x^{3} = 16 x

1 - 9 x - 6 x - x^{3} = 0

6-3(x+1)=-4x^2(1-x)

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

3x^4-3x^3-1x^2=0

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

z \cdot z^{3} + 15 = 16.66