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人気のある代数 >

x^6+9x^4+24x^2+16=0

解

x^{6} + 9 x^{4} + 24 x^{2} + 16 = 0

解

x = i, x = - i, x = 2 i, x = - 2 i

解答ステップ

x^{6} + 9 x^{4} + 24 x^{2} + 16 = 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} + 9 u^{2} + 24 u + 16 = 0

解く

u^{3} + 9 u^{2} + 24 u + 16 = 0 : u = - 1, u = - 4

u = - 1, u = - 4

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

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

解く

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

解答は

x = i, x = - i, x = 2 i, x = - 2 i

グラフ

人気の例

3x^4+x^3+73x^2+25x+16=0

3 x^{4} + x^{3} + 73 x^{2} + 25 x + 16 = 0

4x^3-51x^2+210x-275=0

4 x^{3} - 51 x^{2} + 210 x - 275 = 0

x^4-4x^3+10x^2-12x+5=0

x^{4} - 4 x^{3} + 10 x^{2} - 12 x + 5 = 0

x^3+x^2-56x+144=0

x^{3} + x^{2} - 56 x + 144 = 0

x^4-5x^3-6x^2+7x-2=0

x^{4} - 5 x^{3} - 6 x^{2} + 7 x - 2 = 0