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人気のある代数 >

x^8-15x^4-16=0

解

x^{8} - 15 x^{4} - 16 = 0

解

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

解答ステップ

x^{8} - 15 x^{4} - 16 = 0

equationを

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

と以下で書き換える:

u^{4} = x^{8}

u^{4} - 15 u^{2} - 16 = 0

解く

u^{4} - 15 u^{2} - 16 = 0 : u = 4, u = - 4, u = i, u = - i

u = 4, u = - 4, u = i, u = - i

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = 4 : x = 2, x = - 2

解く

x^{2} = - 4 : x = 2 i, x = - 2 i

解く

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

解く

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

解答は

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

グラフ

人気の例

- 2 x^{4} + 7 = 2 x + 5

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

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

x^{3} + 16 x = 0

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

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

9 x^{6} = 36 x^{4}