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人気のある代数 >

x^9=1

解

x^{9} = 1

解

x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = cos (\frac{2 π}{9}) + i sin (\frac{2 π}{9}), x = cos (\frac{8 π}{9}) + i sin (\frac{8 π}{9}), x = cos (\frac{14 π}{9}) + i sin (\frac{14 π}{9}), x = cos (\frac{2 π}{9}) - i sin (\frac{2 π}{9}), x = cos (\frac{4 π}{9}) + i sin (\frac{4 π}{9}), x = cos (\frac{10 π}{9}) + i sin (\frac{10 π}{9})

解答ステップ

x^{9} = 1

equationを

u = x^{3}

と以下で書き換える:

u^{3} = x^{9}

u^{3} = 1

解く

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

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

再び

u = x^{3}

に置き換えて以下を解く:

x

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} = \frac{- 1 + 3 i}{2} : x = cos (\frac{2 π}{9}) + i sin (\frac{2 π}{9}), x = cos (\frac{8 π}{9}) + i sin (\frac{8 π}{9}), x = cos (\frac{14 π}{9}) + i sin (\frac{14 π}{9})

解く

x^{3} = \frac{- 1 - 3 i}{2} : x = cos (\frac{2 π}{9}) - i sin (\frac{2 π}{9}), x = cos (\frac{4 π}{9}) + i sin (\frac{4 π}{9}), x = cos (\frac{10 π}{9}) + i sin (\frac{10 π}{9})

解答は

x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = cos (\frac{2 π}{9}) + i sin (\frac{2 π}{9}), x = cos (\frac{8 π}{9}) + i sin (\frac{8 π}{9}), x = cos (\frac{14 π}{9}) + i sin (\frac{14 π}{9}), x = cos (\frac{2 π}{9}) - i sin (\frac{2 π}{9}), x = cos (\frac{4 π}{9}) + i sin (\frac{4 π}{9}), x = cos (\frac{10 π}{9}) + i sin (\frac{10 π}{9})

グラフ

人気の例

x^3-4x^2-16x+64=0

x^{3} - 4 x^{2} - 16 x + 64 = 0

15x-10=6x-(x^2)(-x^3)

15 x - 10 = 6 x - (x^{2}) (- x^{3})

x^{3} = 1 - i

2 x^{4} - 48 x^{2} = 0

x^{2} - x^{3} = 12