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人気のある代数 >

x^8-2x^4+1=0

解

x^{8} - 2 x^{4} + 1 = 0

解

x = 1, x = - 1, x = i, x = - i

解答ステップ

x^{8} - 2 x^{4} + 1 = 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} - 2 u^{2} + 1 = 0

解く

u^{4} - 2 u^{2} + 1 = 0 : u = 1, u = - 1

u = 1, u = - 1

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

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

解く

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

解答は

x = 1, x = - 1, x = i, x = - i

グラフ

人気の例

4 x^{3} - x = 0

5 x^{4} - 4 x^{2} - 1 = 0

x^4-2x^3+8x-16=0

x^{4} - 2 x^{3} + 8 x - 16 = 0

z^{6} = - 8

solvefor y,x=y^4-y^2

so l v e f or y, x = y^{4} - y^{2}