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人気のある代数 >

4x^4-5x^2+9=0

解

4 x^{4} - 5 x^{2} + 9 = 0

解

x = \frac{17}{4} + \frac{7}{4} i, x = - \frac{17}{4} - \frac{7}{4} i, x = \frac{17}{4} - \frac{7}{4} i, x = - \frac{17}{4} + \frac{7}{4} i

解答ステップ

4 x^{4} - 5 x^{2} + 9 = 0

equationを

u = x^{2}

と以下で書き換える:

u^{2} = x^{4}

4 u^{2} - 5 u + 9 = 0

解く

4 u^{2} - 5 u + 9 = 0 : u = \frac{5}{8} + i \frac{119}{8}, u = \frac{5}{8} - i \frac{119}{8}

u = \frac{5}{8} + i \frac{119}{8}, u = \frac{5}{8} - i \frac{119}{8}

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = \frac{5}{8} + i \frac{119}{8} : x = \frac{17}{4} + \frac{7}{4} i, x = - \frac{17}{4} - \frac{7}{4} i

解く

x^{2} = \frac{5}{8} - i \frac{119}{8} : x = \frac{17}{4} - \frac{7}{4} i, x = - \frac{17}{4} + \frac{7}{4} i

解答は

x = \frac{17}{4} + \frac{7}{4} i, x = - \frac{17}{4} - \frac{7}{4} i, x = \frac{17}{4} - \frac{7}{4} i, x = - \frac{17}{4} + \frac{7}{4} i

グラフ

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