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人気のある代数 >

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

解

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

解

x = \frac{7}{2} + \frac{1}{2} i, x = - \frac{7}{2} - \frac{1}{2} i, x = \frac{7}{2} - \frac{1}{2} i, x = - \frac{7}{2} + \frac{1}{2} i

解答ステップ

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

equationを

u = x^{2}

と以下で書き換える:

u^{2} = x^{4}

u^{2} - 3 u + 4 = 0

解く

u^{2} - 3 u + 4 = 0 : u = \frac{3}{2} + i \frac{7}{2}, u = \frac{3}{2} - i \frac{7}{2}

u = \frac{3}{2} + i \frac{7}{2}, u = \frac{3}{2} - i \frac{7}{2}

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

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

解く

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

解答は

x = \frac{7}{2} + \frac{1}{2} i, x = - \frac{7}{2} - \frac{1}{2} i, x = \frac{7}{2} - \frac{1}{2} i, x = - \frac{7}{2} + \frac{1}{2} i

グラフ

人気の例

2 x^{4} - 2 x^{2} - 12 = 0

2 x (3 x^{2} + 1) = 0

x^3-2x^2+3x-1=0

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

28x^3+88x^2-37x-7=0

28 x^{3} + 88 x^{2} - 37 x - 7 = 0

2x^3-3x^2+4x-5=0

2 x^{3} - 3 x^{2} + 4 x - 5 = 0