371= 4/3 pir^3

Solución

371 = \frac{4}{3} π r^{3}

r = 3 \frac{1113}{4 π}, r = - \frac{4 ^{\frac{2}{3}} 3 1113 π ^{\frac{2}{3}}}{8 π} + i \frac{3 ^{\frac{5}{6}} \cdot 4 ^{\frac{2}{3}} 3 371 π ^{\frac{2}{3}}}{8 π}, r = - \frac{4 ^{\frac{2}{3}} 3 1113 π ^{\frac{2}{3}}}{8 π} - i \frac{3 ^{\frac{5}{6}} \cdot 4 ^{\frac{2}{3}} 3 371 π ^{\frac{2}{3}}}{8 π}

Pasos de solución

371 = \frac{4}{3} π r^{3}

Intercambiar lados

\frac{4}{3} π r^{3} = 371

Simplificar

\frac{4}{3} π : \frac{4 π}{3}

\frac{4 π}{3} r^{3} = 371

Multiplicar ambos lados por

3

4 π r^{3} = 1113

Dividir ambos lados entre

4 π

r^{3} = \frac{1113}{4 π}

Para

x^{3} = f (a)

las soluciones son

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

r = 3 \frac{1113}{4 π}, r = 3 \frac{1113}{4 π} \frac{- 1 + 3 i}{2}, r = 3 \frac{1113}{4 π} \frac{- 1 - 3 i}{2}

Simplificar

3 \frac{1113}{4 π} \frac{- 1 + 3 i}{2} : - \frac{4 ^{\frac{2}{3}} 3 1113 π ^{\frac{2}{3}}}{8 π} + i \frac{3 ^{\frac{5}{6}} \cdot 4 ^{\frac{2}{3}} 3 371 π ^{\frac{2}{3}}}{8 π}

Simplificar

3 \frac{1113}{4 π} \frac{- 1 - 3 i}{2} : - \frac{4 ^{\frac{2}{3}} 3 1113 π ^{\frac{2}{3}}}{8 π} - i \frac{3 ^{\frac{5}{6}} \cdot 4 ^{\frac{2}{3}} 3 371 π ^{\frac{2}{3}}}{8 π}

r = 3 \frac{1113}{4 π}, r = - \frac{4 ^{\frac{2}{3}} 3 1113 π ^{\frac{2}{3}}}{8 π} + i \frac{3 ^{\frac{5}{6}} \cdot 4 ^{\frac{2}{3}} 3 371 π ^{\frac{2}{3}}}{8 π}, r = - \frac{4 ^{\frac{2}{3}} 3 1113 π ^{\frac{2}{3}}}{8 π} - i \frac{3 ^{\frac{5}{6}} \cdot 4 ^{\frac{2}{3}} 3 371 π ^{\frac{2}{3}}}{8 π}

x^{3} - x^{2} + x = 6

\frac{4}{3} π r^{3} = 4 π r^{2}

2 x^{3} - 26 x^{2} + 84 x = 0

n c^{3} - n c^{4} = n c^{1}

4 m^{3} - 40 m^{2} + 36 m = 0