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人気のある代数 >

x^5x-6=39

解

x^{5} x - 6 = 39

解

x = 345, x = - 345, x = \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} + \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i, x = - \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} - \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i, x = \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} - \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i, x = - \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} + \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i

解答ステップ

x^{5} x - 6 = 39

6

を右側に移動します

x^{5} x = 45

簡素化

x^{6} = 45

equationを

u = x^{2}

と以下で書き換える:

u^{3} = x^{6}

u^{3} = 45

解く

u^{3} = 45 : u = 345, u = 345 \frac{- 1 + 3 i}{2}, u = 345 \frac{- 1 - 3 i}{2}

u = 345, u = 345 \frac{- 1 + 3 i}{2}, u = 345 \frac{- 1 - 3 i}{2}

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = 345 : x = 345, x = - 345

解く

x^{2} = 345 \frac{- 1 + 3 i}{2} : x = \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} + \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i, x = - \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} - \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i

解く

x^{2} = 345 \frac{- 1 - 3 i}{2} : x = \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} - \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i, x = - \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} + \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i

解答は

x = 345, x = - 345, x = \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} + \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i, x = - \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} - \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i, x = \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} - \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i, x = - \frac{- 3 45 + 2 4 5 ^{\frac{2}{3}}}{2} + \frac{3 45 3}{2 - 3 45 + 2 4 5 ^{\frac{2}{3}}} i

グラフ

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