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人気のある代数 >

(x^3-6)^2+3(x^3-6)-10=0

解

(x^{3} - 6)^{2} + 3 (x^{3} - 6) - 10 = 0

解

x = 2, x = - 1 + 3 i, x = - 1 - 3 i, x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i

解答ステップ

(x^{3} - 6)^{2} + 3 (x^{3} - 6) - 10 = 0

拡張

(x^{3} - 6)^{2} + 3 (x^{3} - 6) - 10 : x^{6} - 9 x^{3} + 8

x^{6} - 9 x^{3} + 8 = 0

equationを

u = x^{3}

と以下で書き換える:

u^{2} = x^{6}

u^{2} - 9 u + 8 = 0

解く

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

u = 8, u = 1

再び

u = x^{3}

に置き換えて以下を解く:

x

解く

x^{3} = 8 : x = 2, x = - 1 + 3 i, x = - 1 - 3 i

解く

x^{3} = 1 : x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i

解答は

x = 2, x = - 1 + 3 i, x = - 1 - 3 i, x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i

グラフ

人気の例

3 c^{3} + 9 = - 72

y^{3} - 5 y^{2} = 0

z^3+2z^2+21z-58=0

z^{3} + 2 z^{2} + 21 z - 58 = 0

x^3+4x^2-36x-144=0

x^{3} + 4 x^{2} - 36 x - 144 = 0

x^{3} - 9 x^{2} - 4 = 0