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人気のある代数 >

solvefor x,729x^6-4096=0

解

解く

x, 729 x^{6} - 4096 = 0

解

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

解答ステップ

729 x^{6} - 4096 = 0

4096

を右側に移動します

729 x^{6} = 4096

以下で両辺を割る

729

x^{6} = \frac{4096}{729}

equationを

u = x^{2}

と以下で書き換える:

u^{3} = x^{6}

u^{3} = \frac{4096}{729}

解く

u^{3} = \frac{4096}{729} : u = 3 \frac{4096}{729}, u = 3 \frac{4096}{729} \frac{- 1 + 3 i}{2}, u = 3 \frac{4096}{729} \frac{- 1 - 3 i}{2}

u = 3 \frac{4096}{729}, u = 3 \frac{4096}{729} \frac{- 1 + 3 i}{2}, u = 3 \frac{4096}{729} \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} = 3 \frac{4096}{729} : x = \frac{4}{3}, x = - \frac{4}{3}

解く

x^{2} = 3 \frac{4096}{729} \frac{- 1 + 3 i}{2} : x = \frac{2}{3} + \frac{2}{3} i, x = - \frac{2}{3} - \frac{2}{3} i

解く

x^{2} = 3 \frac{4096}{729} \frac{- 1 - 3 i}{2} : x = \frac{2}{3} - \frac{2}{3} i, x = - \frac{2}{3} + \frac{2}{3} i

解答は

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

グラフ

人気の例

solvefor k,k^3-4k^2+k+6=0

so l v e f or k, k^{3} - 4 k^{2} + k + 6 = 0

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

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

f^{6} = 6 + 3

x^4-9x^2+11x-2=0

x^{4} - 9 x^{2} + 11 x - 2 = 0

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