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人気のある代数 >

z^8-2z^4+4=0

解

z^{8} - 2 z^{4} + 4 = 0

解

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

解答ステップ

z^{8} - 2 z^{4} + 4 = 0

equationを

u = z^{2}, u^{2} = z^{4}

と以下で書き換える:

u^{4} = z^{8}

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

解く

u^{4} - 2 u^{2} + 4 = 0 : u = \frac{3}{2} + \frac{1}{2} i, u = - \frac{3}{2} - \frac{1}{2} i, u = - \frac{3}{2} + \frac{1}{2} i, u = \frac{3}{2} - \frac{1}{2} i

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

解く

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

解く

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

解く

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

解答は

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

グラフ

人気の例

(x^2+2x)^2-2(x^2+2x)-3=0

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

4x^3-15x^2+12x=0

4 x^{3} - 15 x^{2} + 12 x = 0

x^{7} = - 128

12x^3-91x^2+50x-7=0

12 x^{3} - 91 x^{2} + 50 x - 7 = 0

根 x^3+3x^2-4x-12

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