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人気のある代数 >

z^4+2z^2=sqrt(3)i

解

z^{4} + 2 z^{2} = 3 i

解

z = \frac{1}{2 2 3 - 6 + 2 - 6} + \frac{2 3 - 6 + 2 - 6}{2} i, z = - \frac{1}{2 2 3 - 6 + 2 - 6} - \frac{2 3 - 6 + 2 - 6}{2} i, z = - \frac{1}{2 2 3 + 6 + 6 + 2} + \frac{2 3 + 6 + 6 + 2}{2} i, z = - \frac{1}{2 ( - 2 3 + 6 + 6 + 2 )} - \frac{2 3 + 6 + 6 + 2}{2} i

解答ステップ

z^{4} + 2 z^{2} = 3 i

3 i

を左側に移動します

(z^{4} + 2 z^{2}) - 3 i = 0

標準的な形式で書く

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

z^{4} + 2 z^{2} - 3 i = 0

equationを

u = z^{2}

と以下で書き換える:

u^{2} = z^{4}

u^{2} + 2 u - 3 i = 0

解く

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

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

再び

u = z^{2}

に置き換えて以下を解く:

z

解く

z^{2} = \frac{3 - 2}{2} + \frac{1}{2} i : z = \frac{1}{2 2 3 - 6 + 2 - 6} + \frac{2 3 - 6 + 2 - 6}{2} i, z = - \frac{1}{2 2 3 - 6 + 2 - 6} - \frac{2 3 - 6 + 2 - 6}{2} i

解く

z^{2} = - \frac{3 + 2}{2} - \frac{1}{2} i : z = - \frac{1}{2 2 3 + 6 + 6 + 2} + \frac{2 3 + 6 + 6 + 2}{2} i, z = - \frac{1}{2 ( - 2 3 + 6 + 6 + 2 )} - \frac{2 3 + 6 + 6 + 2}{2} i

解答は

z = \frac{1}{2 2 3 - 6 + 2 - 6} + \frac{2 3 - 6 + 2 - 6}{2} i, z = - \frac{1}{2 2 3 - 6 + 2 - 6} - \frac{2 3 - 6 + 2 - 6}{2} i, z = - \frac{1}{2 2 3 + 6 + 6 + 2} + \frac{2 3 + 6 + 6 + 2}{2} i, z = - \frac{1}{2 ( - 2 3 + 6 + 6 + 2 )} - \frac{2 3 + 6 + 6 + 2}{2} i

人気の例

185 = 5 x^{3}

X^{3} - X^{2} - 4 X + 4 = 0

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

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

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

x^{3} + 6 = 12