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人気のある代数 >

x^6-9x^2-8x^4=0

解

x^{6} - 9 x^{2} - 8 x^{4} = 0

解

x = 0, x = i, x = - i, x = 3, x = - 3

解答ステップ

x^{6} - 9 x^{2} - 8 x^{4} = 0

標準的な形式で書く

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

x^{6} - 8 x^{4} - 9 x^{2} = 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} - 8 u^{2} - 9 u = 0

解く

u^{3} - 8 u^{2} - 9 u = 0 : u = 0, u = - 1, u = 9

u = 0, u = - 1, u = 9

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = 0 : x = 0

解く

x^{2} = - 1 : x = i, x = - i

解く

x^{2} = 9 : x = 3, x = - 3

解答は

x = 0, x = i, x = - i, x = 3, x = - 3

グラフ

人気の例

2 x^{3} - 50 x = 0

solvefor a,54=a^4

so l v e f or a, 54 = a^{4}

p(2p-5)^2-3(2p-5)=0

p (2 p - 5)^{2} - 3 (2 p - 5) = 0

x^3-6x^2-15x+40=0

x^{3} - 6 x^{2} - 15 x + 40 = 0

(12x-1)(6x-1)(4x-1)(3x-1)=5

(12 x - 1) (6 x - 1) (4 x - 1) (3 x - 1) = 5