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人気のある代数 >

x^4+5x^2+16=0

解

x^{4} + 5 x^{2} + 16 = 0

解

x = \frac{3}{2} + \frac{13}{2} i, x = - \frac{3}{2} - \frac{13}{2} i, x = \frac{3}{2} - \frac{13}{2} i, x = - \frac{3}{2} + \frac{13}{2} i

解答ステップ

x^{4} + 5 x^{2} + 16 = 0

equationを

u = x^{2}

と以下で書き換える:

u^{2} = x^{4}

u^{2} + 5 u + 16 = 0

解く

u^{2} + 5 u + 16 = 0 : u = - \frac{5}{2} + i \frac{39}{2}, u = - \frac{5}{2} - i \frac{39}{2}

u = - \frac{5}{2} + i \frac{39}{2}, u = - \frac{5}{2} - i \frac{39}{2}

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = - \frac{5}{2} + i \frac{39}{2} : x = \frac{3}{2} + \frac{13}{2} i, x = - \frac{3}{2} - \frac{13}{2} i

解く

x^{2} = - \frac{5}{2} - i \frac{39}{2} : x = \frac{3}{2} - \frac{13}{2} i, x = - \frac{3}{2} + \frac{13}{2} i

解答は

x = \frac{3}{2} + \frac{13}{2} i, x = - \frac{3}{2} - \frac{13}{2} i, x = \frac{3}{2} - \frac{13}{2} i, x = - \frac{3}{2} + \frac{13}{2} i

グラフ

人気の例

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