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人気のある代数 >

x^6+28x^3+16=0

解

x^{6} + 28 x^{3} + 16 = 0

解

x = 3 2 (35 - 7), x = - 3 2 (35 - 7) \frac{1}{2} + 3 2 (35 - 7) \frac{3}{2} i, x = - 3 2 (35 - 7) \frac{1}{2} - 3 2 (35 - 7) \frac{3}{2} i, x = 32 3 - 7 - 35, x = - 3 \frac{- 7 - 3 5}{4} + i \frac{3 2 3 3 - 7 - 3 5}{2}, x = - 3 \frac{- 7 - 3 5}{4} - i \frac{3 2 3 3 - 7 - 3 5}{2}

解答ステップ

x^{6} + 28 x^{3} + 16 = 0

equationを

u = x^{3}

と以下で書き換える:

u^{2} = x^{6}

u^{2} + 28 u + 16 = 0

解く

u^{2} + 28 u + 16 = 0 : u = 2 (35 - 7), u = - 2 (7 + 35)

u = 2 (35 - 7), u = - 2 (7 + 35)

再び

u = x^{3}

に置き換えて以下を解く:

x

解く

x^{3} = 2 (35 - 7) : x = 3 2 (35 - 7), x = - 3 2 (35 - 7) \frac{1}{2} + 3 2 (35 - 7) \frac{3}{2} i, x = - 3 2 (35 - 7) \frac{1}{2} - 3 2 (35 - 7) \frac{3}{2} i

解く

x^{3} = - 2 (7 + 35) : x = 32 3 - 7 - 35, x = - 3 \frac{- 7 - 3 5}{4} + i \frac{3 2 3 3 - 7 - 3 5}{2}, x = - 3 \frac{- 7 - 3 5}{4} - i \frac{3 2 3 3 - 7 - 3 5}{2}

解答は

x = 3 2 (35 - 7), x = - 3 2 (35 - 7) \frac{1}{2} + 3 2 (35 - 7) \frac{3}{2} i, x = - 3 2 (35 - 7) \frac{1}{2} - 3 2 (35 - 7) \frac{3}{2} i, x = 32 3 - 7 - 35, x = - 3 \frac{- 7 - 3 5}{4} + i \frac{3 2 3 3 - 7 - 3 5}{2}, x = - 3 \frac{- 7 - 3 5}{4} - i \frac{3 2 3 3 - 7 - 3 5}{2}

グラフ

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