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人気のある代数 >

x^6-2x^3+4=16

解

x^{6} - 2 x^{3} + 4 = 16

解

x = 3 1 + 13, x = - 3 1 + 13 \frac{1}{2} + 3 1 + 13 \frac{3}{2} i, x = - 3 1 + 13 \frac{1}{2} - 3 1 + 13 \frac{3}{2} i, x = 3 1 - 13, x = - 3 1 - 13 \frac{1}{2} + 3 1 - 13 \frac{3}{2} i, x = - 3 1 - 13 \frac{1}{2} - 3 1 - 13 \frac{3}{2} i

解答ステップ

x^{6} - 2 x^{3} + 4 = 16

16

を左側に移動します

x^{6} - 2 x^{3} - 12 = 0

equationを

u = x^{3}

と以下で書き換える:

u^{2} = x^{6}

u^{2} - 2 u - 12 = 0

解く

u^{2} - 2 u - 12 = 0 : u = 1 + 13, u = 1 - 13

u = 1 + 13, u = 1 - 13

再び

u = x^{3}

に置き換えて以下を解く:

x

解く

x^{3} = 1 + 13 : x = 3 1 + 13, x = - 3 1 + 13 \frac{1}{2} + 3 1 + 13 \frac{3}{2} i, x = - 3 1 + 13 \frac{1}{2} - 3 1 + 13 \frac{3}{2} i

解く

x^{3} = 1 - 13 : x = 3 1 - 13, x = - 3 1 - 13 \frac{1}{2} + 3 1 - 13 \frac{3}{2} i, x = - 3 1 - 13 \frac{1}{2} - 3 1 - 13 \frac{3}{2} i

解答は

x = 3 1 + 13, x = - 3 1 + 13 \frac{1}{2} + 3 1 + 13 \frac{3}{2} i, x = - 3 1 + 13 \frac{1}{2} - 3 1 + 13 \frac{3}{2} i, x = 3 1 - 13, x = - 3 1 - 13 \frac{1}{2} + 3 1 - 13 \frac{3}{2} i, x = - 3 1 - 13 \frac{1}{2} - 3 1 - 13 \frac{3}{2} i

グラフ

人気の例

x - x^{4} = 0

x^3-8x^2+17x-4=0

x^{3} - 8 x^{2} + 17 x - 4 = 0

6x^3+9x^2+4x+6=0

6 x^{3} + 9 x^{2} + 4 x + 6 = 0

-x^3-3x^2+9x+27=0

- x^{3} - 3 x^{2} + 9 x + 27 = 0

x^4-3x^2+4x+1=0

x^{4} - 3 x^{2} + 4 x + 1 = 0