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人気のある代数 >

z^6-12=0

解

z^{6} - 12 = 0

解

z = 312, z = - 312, z = 0.75654 \dots + \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i, z = - 0.75654 \dots - \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i, z = 0.75654 \dots - \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i, z = - 0.75654 \dots + \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i

解答ステップ

z^{6} - 12 = 0

12

を右側に移動します

z^{6} = 12

equationを

u = z^{2}

と以下で書き換える:

u^{3} = z^{6}

u^{3} = 12

解く

u^{3} = 12 : u = 312, u = 312 \frac{- 1 + 3 i}{2}, u = 312 \frac{- 1 - 3 i}{2}

u = 312, u = 312 \frac{- 1 + 3 i}{2}, u = 312 \frac{- 1 - 3 i}{2}

再び

u = z^{2}

に置き換えて以下を解く:

z

解く

z^{2} = 312 : z = 312, z = - 312

解く

z^{2} = 312 \frac{- 1 + 3 i}{2} : z = 0.75654 \dots + \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i, z = - 0.75654 \dots - \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i

解く

z^{2} = 312 \frac{- 1 - 3 i}{2} : z = 0.75654 \dots - \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i, z = - 0.75654 \dots + \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i

解答は

z = 312, z = - 312, z = 0.75654 \dots + \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i, z = - 0.75654 \dots - \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i, z = 0.75654 \dots - \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i, z = - 0.75654 \dots + \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i

グラフ

人気の例

-λ^3+12λ^2-21λ+10=0

- λ^{3} + 12 λ^{2} - 21 λ + 10 = 0

x^4+2x^3-11x^2-12x+36=0

x^{4} + 2 x^{3} - 11 x^{2} - 12 x + 36 = 0

x^{2} + x^{10} = 0

4 \cdot x^{3} = 32

solvefor x,xx^2+y^2=0

so l v e f or x, x x^{2} + y^{2} = 0