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人気のある代数 >

2z^6-15z^3-27=0

解

2 z^{6} - 15 z^{3} - 27 = 0

解

z = 39, z = - 39 \frac{1}{2} + 39 \frac{3}{2} i, z = - 39 \frac{1}{2} - 39 \frac{3}{2} i, z = - 3 \frac{3}{2}, z = \frac{3 3}{2 3 2} - \frac{6 3 ^{5}}{2 3 2} i, z = \frac{3 3}{2 3 2} + \frac{6 3 ^{5}}{2 3 2} i

解答ステップ

2 z^{6} - 15 z^{3} - 27 = 0

equationを

u = z^{3}

と以下で書き換える:

u^{2} = z^{6}

2 u^{2} - 15 u - 27 = 0

解く

2 u^{2} - 15 u - 27 = 0 : u = 9, u = - \frac{3}{2}

u = 9, u = - \frac{3}{2}

再び

u = z^{3}

に置き換えて以下を解く:

z

解く

z^{3} = 9 : z = 39, z = - 39 \frac{1}{2} + 39 \frac{3}{2} i, z = - 39 \frac{1}{2} - 39 \frac{3}{2} i

解く

z^{3} = - \frac{3}{2} : z = - 3 \frac{3}{2}, z = \frac{3 3}{2 3 2} - \frac{6 3 ^{5}}{2 3 2} i, z = \frac{3 3}{2 3 2} + \frac{6 3 ^{5}}{2 3 2} i

解答は

z = 39, z = - 39 \frac{1}{2} + 39 \frac{3}{2} i, z = - 39 \frac{1}{2} - 39 \frac{3}{2} i, z = - 3 \frac{3}{2}, z = \frac{3 3}{2 3 2} - \frac{6 3 ^{5}}{2 3 2} i, z = \frac{3 3}{2 3 2} + \frac{6 3 ^{5}}{2 3 2} i

グラフ

人気の例

(x^2+7x+49)(x-7)=218

(x^{2} + 7 x + 49) (x - 7) = 218

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

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

x^{3} + 3 x^{2} - 58 = 0

(x+2)^2=x(x^2-10x+25)

(x + 2)^{2} = x (x^{2} - 10 x + 25)

w+w^2-w^3+w^4=5

w + w^{2} - w^{3} + w^{4} = 5