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人気のある代数 >

6=-w^8

解

6 = - w^{8}

解

w = \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} + \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i, w = - \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} - \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i, w = - \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} + \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} - \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} + \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = - \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} - \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = - \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} + \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i, w = \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} - \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i

解答ステップ

6 = - w^{8}

辺を交換する

- w^{8} = 6

以下で両辺を割る

- 1

w^{8} = - 6

equationを

u = w^{2}

と以下で書き換える:

u^{4} = w^{8}

u^{4} = - 6

解く

u^{4} = - 6 : u = 4 \frac{3}{2} + 4 \frac{3}{2} i, u = - 4 \frac{3}{2} - 4 \frac{3}{2} i, u = - 4 \frac{3}{2} + 4 \frac{3}{2} i, u = 4 \frac{3}{2} - 4 \frac{3}{2} i

u = 4 \frac{3}{2} + 4 \frac{3}{2} i, u = - 4 \frac{3}{2} - 4 \frac{3}{2} i, u = - 4 \frac{3}{2} + 4 \frac{3}{2} i, u = 4 \frac{3}{2} - 4 \frac{3}{2} i

再び

u = w^{2}

に置き換えて以下を解く:

w

解く

w^{2} = 4 \frac{3}{2} + 4 \frac{3}{2} i : w = \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} + \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i, w = - \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} - \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i

解く

w^{2} = - 4 \frac{3}{2} - 4 \frac{3}{2} i : w = - \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} + \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} - \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i

解く

w^{2} = - 4 \frac{3}{2} + 4 \frac{3}{2} i : w = \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} + \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = - \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} - \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i

解く

w^{2} = 4 \frac{3}{2} - 4 \frac{3}{2} i : w = - \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} + \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i, w = \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} - \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i

解答は

w = \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} + \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i, w = - \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} - \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i, w = - \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} + \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} - \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} + \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = - \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} - \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = - \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} + \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i, w = \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} - \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i

グラフ

人気の例

x^3-4x^2-5x+20=0

x^{3} - 4 x^{2} - 5 x + 20 = 0

x^{4} - 21 x^{2} + 80 = 0

x^{3} + 5 x^{2} = - 6 x

solvefor x,x^3-2x^2-5x+6=0

so l v e f or x, x^{3} - 2 x^{2} - 5 x + 6 = 0

solvefor F,t=(F^3+G)a

so l v e f or F, t = (F^{3} + G) a