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人気のある代数 >

12x^4-4x^2-1=0

解

12 x^{4} - 4 x^{2} - 1 = 0

解

x = \frac{1}{2}, x = - \frac{1}{2}, x = \frac{1}{6} i, x = - \frac{1}{6} i

解答ステップ

12 x^{4} - 4 x^{2} - 1 = 0

equationを

u = x^{2}

と以下で書き換える:

u^{2} = x^{4}

12 u^{2} - 4 u - 1 = 0

解く

12 u^{2} - 4 u - 1 = 0 : u = \frac{1}{2}, u = - \frac{1}{6}

u = \frac{1}{2}, u = - \frac{1}{6}

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = \frac{1}{2} : x = \frac{1}{2}, x = - \frac{1}{2}

解く

x^{2} = - \frac{1}{6} : x = \frac{1}{6} i, x = - \frac{1}{6} i

解答は

x = \frac{1}{2}, x = - \frac{1}{2}, x = \frac{1}{6} i, x = - \frac{1}{6} i

グラフ

人気の例

2 - x = x^{3}

(x^2-6)(x^2+1)=0

(x^{2} - 6) (x^{2} + 1) = 0

x^{4} + 16 = 2 x^{3} + 8 x

4x^3+8x^2-9x=18

4 x^{3} + 8 x^{2} - 9 x = 18

x^{2} (2 x^{2} + 6) = 8