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人気のある代数 >

9x^8-9=0

解

9 x^{8} - 9 = 0

解

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

解答ステップ

9 x^{8} - 9 = 0

9

を右側に移動します

9 x^{8} = 9

以下で両辺を割る

9

x^{8} = 1

equationを

u = x^{2}

と以下で書き換える:

u^{4} = x^{8}

u^{4} = 1

解く

u^{4} = 1 : u = 1, u = - 1, u = i, u = - i

u = 1, u = - 1, 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} = 1 : x = 1, x = - 1

解く

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

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

グラフ

人気の例

x^3-2x^2+x+18=0

x^{3} - 2 x^{2} + x + 18 = 0

x^{4} = 80

4x^3-69x^2+378x-637=0

4 x^{3} - 69 x^{2} + 378 x - 637 = 0

3x^4+5x^3-12x^2-20x=0

3 x^{4} + 5 x^{3} - 12 x^{2} - 20 x = 0

6 b^{3} - 9 b^{2} + 2 = 0