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人気のある代数 >

42x^4-x^2-1=0

解

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

解

x = \frac{1}{6}, x = - \frac{1}{6}, x = \frac{1}{7} i, x = - \frac{1}{7} i

解答ステップ

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

equationを

u = x^{2}

と以下で書き換える:

u^{2} = x^{4}

42 u^{2} - u - 1 = 0

解く

42 u^{2} - u - 1 = 0 : u = \frac{1}{6}, u = - \frac{1}{7}

u = \frac{1}{6}, u = - \frac{1}{7}

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

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

解く

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

解答は

x = \frac{1}{6}, x = - \frac{1}{6}, x = \frac{1}{7} i, x = - \frac{1}{7} i

グラフ

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