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人気のある代数 >

x^8-16=15x^4

解

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

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} - 16 = 15 x^{4}

15 x^{4}

を左側に移動します

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

標準的な形式で書く

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

x^{3} = 25

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

z^{5} = 32 i

-x^3+3x^2-3x+1=0

- x^{3} + 3 x^{2} - 3 x + 1 = 0

4 x^{3} - 2 x = 0