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人気のある代数 >

x^6+3x^3-6=0

解

x^{6} + 3 x^{3} - 6 = 0

解

x = 3 \frac{- 3 + 33}{2}, x = - 3 \frac{- 3 + 33}{2} \frac{1}{2} + 3 \frac{- 3 + 33}{2} \frac{3}{2} i, x = - 3 \frac{- 3 + 33}{2} \frac{1}{2} - 3 \frac{- 3 + 33}{2} \frac{3}{2} i, x = 3 \frac{- 3 - 33}{2}, x = - 3 \frac{- 3 - 33}{2} \frac{1}{2} + 3 \frac{- 3 - 33}{2} \frac{3}{2} i, x = - 3 \frac{- 3 - 33}{2} \frac{1}{2} - 3 \frac{- 3 - 33}{2} \frac{3}{2} i

解答ステップ

x^{6} + 3 x^{3} - 6 = 0

equationを

u = x^{3}

と以下で書き換える:

u^{2} = x^{6}

u^{2} + 3 u - 6 = 0

解く

u^{2} + 3 u - 6 = 0 : u = \frac{- 3 + 33}{2}, u = \frac{- 3 - 33}{2}

u = \frac{- 3 + 33}{2}, u = \frac{- 3 - 33}{2}

再び

u = x^{3}

に置き換えて以下を解く:

x

解く

x^{3} = \frac{- 3 + 33}{2} : x = 3 \frac{- 3 + 33}{2}, x = - 3 \frac{- 3 + 33}{2} \frac{1}{2} + 3 \frac{- 3 + 33}{2} \frac{3}{2} i, x = - 3 \frac{- 3 + 33}{2} \frac{1}{2} - 3 \frac{- 3 + 33}{2} \frac{3}{2} i

解く

x^{3} = \frac{- 3 - 33}{2} : x = 3 \frac{- 3 - 33}{2}, x = - 3 \frac{- 3 - 33}{2} \frac{1}{2} + 3 \frac{- 3 - 33}{2} \frac{3}{2} i, x = - 3 \frac{- 3 - 33}{2} \frac{1}{2} - 3 \frac{- 3 - 33}{2} \frac{3}{2} i

解答は

x = 3 \frac{- 3 + 33}{2}, x = - 3 \frac{- 3 + 33}{2} \frac{1}{2} + 3 \frac{- 3 + 33}{2} \frac{3}{2} i, x = - 3 \frac{- 3 + 33}{2} \frac{1}{2} - 3 \frac{- 3 + 33}{2} \frac{3}{2} i, x = 3 \frac{- 3 - 33}{2}, x = - 3 \frac{- 3 - 33}{2} \frac{1}{2} + 3 \frac{- 3 - 33}{2} \frac{3}{2} i, x = - 3 \frac{- 3 - 33}{2} \frac{1}{2} - 3 \frac{- 3 - 33}{2} \frac{3}{2} i

グラフ

人気の例

x^{4} + 3 x^{2} + 1 = 0

80=-0.001x^3+0.18x^2+60

80 = - 0.001 x^{3} + 0.18 x^{2} + 60

1 - z + z^{2} - z^{3} = 0

50+2((x-2)/4)^3=300

50 + 2 (\frac{x - 2}{4})^{3} = 300

z^{3} = \frac{1}{8 i}