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人気のある代数 >

20x^4+160x^2-285=0

解

20 x^{4} + 160 x^{2} - 285 = 0

解

x = \frac{3}{2}, x = - \frac{3}{2}, x = \frac{19}{2} i, x = - \frac{19}{2} i

解答ステップ

20 x^{4} + 160 x^{2} - 285 = 0

equationを

u = x^{2}

と以下で書き換える:

u^{2} = x^{4}

20 u^{2} + 160 u - 285 = 0

解く

20 u^{2} + 160 u - 285 = 0 : u = \frac{3}{2}, u = - \frac{19}{2}

u = \frac{3}{2}, u = - \frac{19}{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} : x = \frac{3}{2}, x = - \frac{3}{2}

解く

x^{2} = - \frac{19}{2} : x = \frac{19}{2} i, x = - \frac{19}{2} i

解答は

x = \frac{3}{2}, x = - \frac{3}{2}, x = \frac{19}{2} i, x = - \frac{19}{2} i

グラフ

人気の例

59= 1/4 (75x-x^3)

59 = \frac{1}{4} (75 x - x^{3})

x^4-8x^3+23x^2-28x+12=0

x^{4} - 8 x^{3} + 23 x^{2} - 28 x + 12 = 0

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6 x^{4} + x^{3} - 22 x^{2} - 11 x + 6 = 0

(x^2+3x)^2-2(x^2+3x)-8=0

(x^{2} + 3 x)^{2} - 2 (x^{2} + 3 x) - 8 = 0

216 x = x^{4}