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人気のある代数 >

x^6-14x^4+3x^2-42=0

解

x^{6} - 14 x^{4} + 3 x^{2} - 42 = 0

解

x = 14, x = - 14, x = \frac{4 3}{2} + \frac{4 3}{2} i, x = - \frac{4 3}{2} - \frac{4 3}{2} i, x = \frac{4 3}{2} - \frac{4 3}{2} i, x = - \frac{4 3}{2} + \frac{4 3}{2} i

解答ステップ

x^{6} - 14 x^{4} + 3 x^{2} - 42 = 0

equationを

u = x^{2}, u^{2} = x^{4}

と以下で書き換える:

u^{3} = x^{6}

u^{3} - 14 u^{2} + 3 u - 42 = 0

解く

u^{3} - 14 u^{2} + 3 u - 42 = 0 : u = 14, u = 3 i, u = - 3 i

u = 14, u = 3 i, u = - 3 i

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = 14 : x = 14, x = - 14

解く

x^{2} = 3 i : x = \frac{4 3}{2} + \frac{4 3}{2} i, x = - \frac{4 3}{2} - \frac{4 3}{2} i

解く

x^{2} = - 3 i : x = \frac{4 3}{2} - \frac{4 3}{2} i, x = - \frac{4 3}{2} + \frac{4 3}{2} i

解答は

x = 14, x = - 14, x = \frac{4 3}{2} + \frac{4 3}{2} i, x = - \frac{4 3}{2} - \frac{4 3}{2} i, x = \frac{4 3}{2} - \frac{4 3}{2} i, x = - \frac{4 3}{2} + \frac{4 3}{2} i

グラフ

人気の例

x^4-x^3-13x^2+x+12=0

x^{4} - x^{3} - 13 x^{2} + x + 12 = 0

s^3+10.6s^2+7s+10=0

s^{3} + 10.6 s^{2} + 7 s + 10 = 0

200x-0.02x^2-0.000002x^3-80000=0

200 x - 0.02 x^{2} - 0.000002 x^{3} - 80000 = 0

2x^3-14x^2+2x-14=0

2 x^{3} - 14 x^{2} + 2 x - 14 = 0

24x^3+46x^2+9x-9=0

24 x^{3} + 46 x^{2} + 9 x - 9 = 0