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人気のある代数 >

1-x^9=(1-x)(1+x+x^2)

解

1 - x^{9} = (1 - x) (1 + x + x^{2})

解

x = 0, x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} i, x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i

解答ステップ

1 - x^{9} = (1 - x) (1 + x + x^{2})

拡張

(1 - x) (1 + x + x^{2}) : - x^{3} + 1

1 - x^{9} = - x^{3} + 1

1

を左側に移動します

- x^{9} = - x^{3}

x^{3}

を左側に移動します

- x^{9} + x^{3} = 0

equationを

u = x^{3}

と以下で書き換える:

u^{3} = x^{9}

- u^{3} + u = 0

解く

- u^{3} + u = 0 : u = 0, u = - 1, u = 1

u = 0, u = - 1, u = 1

再び

u = x^{3}

に置き換えて以下を解く:

x

解く

x^{3} = 0 : x = 0

解く

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

解く

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

解答は

x = 0, x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} i, x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i

グラフ

人気の例

x^{4} - 81 = 0

x^{4} - 6 x^{2} + 5 = 0

(x)=3x^3+x^2-22x+9

(x) = 3 x^{3} + x^{2} - 22 x + 9

280xx-xx^7-x=250

280 xx - x x^{7} - x = 250

x^5+x^4-4x^3-4x^2+11x-5=0

x^{5} + x^{4} - 4 x^{3} - 4 x^{2} + 11 x - 5 = 0