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受欢迎的代数 >

solvefor r,x= 2/3 pir^3

解答

求解

r, x = \frac{2}{3} π r^{3}

解答

r = 3 \frac{3 x}{2 π}, r = - \frac{2 ^{\frac{2}{3}} 3 3 π ^{\frac{2}{3}} 3 x}{4 π} + i \frac{2 ^{\frac{2}{3}} \cdot 3 ^{\frac{5}{6}} π ^{\frac{2}{3}} 3 x}{4 π}, r = - \frac{2 ^{\frac{2}{3}} 3 3 π ^{\frac{2}{3}} 3 x}{4 π} - i \frac{2 ^{\frac{2}{3}} \cdot 3 ^{\frac{5}{6}} π ^{\frac{2}{3}} 3 x}{4 π}

求解步骤

x = \frac{2}{3} π r^{3}

交换两边

\frac{2}{3} π r^{3} = x

化简

\frac{2}{3} π : \frac{2 π}{3}

\frac{2 π}{3} r^{3} = x

在两边乘以

3

2 π r^{3} = 3 x

两边除以

2 π

r^{3} = \frac{3 x}{2 π}

对于

x^{3} = f (a)

解为

x = 3 f (a), 3 f (a) \frac{- 1 - 3 i}{2}, 3 f (a) \frac{- 1 + 3 i}{2}

r = 3 \frac{3 x}{2 π}, r = 3 \frac{3 x}{2 π} \frac{- 1 + 3 i}{2}, r = 3 \frac{3 x}{2 π} \frac{- 1 - 3 i}{2}

化简

3 \frac{3 x}{2 π} \frac{- 1 + 3 i}{2} : - \frac{2 ^{\frac{2}{3}} 3 3 π ^{\frac{2}{3}} 3 x}{4 π} + i \frac{2 ^{\frac{2}{3}} \cdot 3 ^{\frac{5}{6}} π ^{\frac{2}{3}} 3 x}{4 π}

化简

3 \frac{3 x}{2 π} \frac{- 1 - 3 i}{2} : - \frac{2 ^{\frac{2}{3}} 3 3 π ^{\frac{2}{3}} 3 x}{4 π} - i \frac{2 ^{\frac{2}{3}} \cdot 3 ^{\frac{5}{6}} π ^{\frac{2}{3}} 3 x}{4 π}

r = 3 \frac{3 x}{2 π}, r = - \frac{2 ^{\frac{2}{3}} 3 3 π ^{\frac{2}{3}} 3 x}{4 π} + i \frac{2 ^{\frac{2}{3}} \cdot 3 ^{\frac{5}{6}} π ^{\frac{2}{3}} 3 x}{4 π}, r = - \frac{2 ^{\frac{2}{3}} 3 3 π ^{\frac{2}{3}} 3 x}{4 π} - i \frac{2 ^{\frac{2}{3}} \cdot 3 ^{\frac{5}{6}} π ^{\frac{2}{3}} 3 x}{4 π}

作图

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