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人気のある代数 >

6z^8+j^5z^4+6=0

解

6 z^{8} + j^{5} z^{4} + 6 = 0

解

z = \frac{- j ^{5} + j ^{10} - 144}{2 4 3}, z = - \frac{- j ^{5} + j ^{10} - 144}{2 4 3}, z = i \frac{3 - 144 + j ^{10} - j ^{5}}{6}, z = - i \frac{3 - 144 + j ^{10} - j ^{5}}{6}, z = \frac{- j ^{5} - j ^{10} - 144}{2 4 3}, z = - \frac{- j ^{5} - j ^{10} - 144}{2 4 3}, z = i \frac{3 - - 144 + j ^{10} - j ^{5}}{6}, z = - i \frac{3 - - 144 + j ^{10} - j ^{5}}{6}

解答ステップ

6 z^{8} + j^{5} z^{4} + 6 = 0

equationを

u = z^{2}, u^{2} = z^{4}

と以下で書き換える:

u^{4} = z^{8}

6 u^{4} + j^{5} u^{2} + 6 = 0

解く

6 u^{4} + j^{5} u^{2} + 6 = 0 : u = \frac{- j ^{5} + j ^{10} - 144}{2 3}, u = - \frac{- j ^{5} + j ^{10} - 144}{2 3}, u = \frac{- j ^{5} - j ^{10} - 144}{2 3}, u = - \frac{- j ^{5} - j ^{10} - 144}{2 3}

u = \frac{- j ^{5} + j ^{10} - 144}{2 3}, u = - \frac{- j ^{5} + j ^{10} - 144}{2 3}, u = \frac{- j ^{5} - j ^{10} - 144}{2 3}, u = - \frac{- j ^{5} - j ^{10} - 144}{2 3}

再び

u = z^{2}

に置き換えて以下を解く:

z

解く

z^{2} = \frac{- j ^{5} + j ^{10} - 144}{2 3} : z = \frac{- j ^{5} + j ^{10} - 144}{2 4 3}, z = - \frac{- j ^{5} + j ^{10} - 144}{2 4 3}

解く

z^{2} = - \frac{- j ^{5} + j ^{10} - 144}{2 3} : z = i \frac{3 - 144 + j ^{10} - j ^{5}}{6}, z = - i \frac{3 - 144 + j ^{10} - j ^{5}}{6}

解く

z^{2} = \frac{- j ^{5} - j ^{10} - 144}{2 3} : z = \frac{- j ^{5} - j ^{10} - 144}{2 4 3}, z = - \frac{- j ^{5} - j ^{10} - 144}{2 4 3}

解く

z^{2} = - \frac{- j ^{5} - j ^{10} - 144}{2 3} : z = i \frac{3 - - 144 + j ^{10} - j ^{5}}{6}, z = - i \frac{3 - - 144 + j ^{10} - j ^{5}}{6}

解答は

z = \frac{- j ^{5} + j ^{10} - 144}{2 4 3}, z = - \frac{- j ^{5} + j ^{10} - 144}{2 4 3}, z = i \frac{3 - 144 + j ^{10} - j ^{5}}{6}, z = - i \frac{3 - 144 + j ^{10} - j ^{5}}{6}, z = \frac{- j ^{5} - j ^{10} - 144}{2 4 3}, z = - \frac{- j ^{5} - j ^{10} - 144}{2 4 3}, z = i \frac{3 - - 144 + j ^{10} - j ^{5}}{6}, z = - i \frac{3 - - 144 + j ^{10} - j ^{5}}{6}

グラフ

人気の例

n^{3} = 125

(x+2)(x-3)(x+1)(x+6)=-36

(x + 2) (x - 3) (x + 1) (x + 6) = - 36

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

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

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

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