972= 4/6 pir^3

Solución

972 = \frac{4}{6} π r^{3}

r = \frac{9 3 2}{3 π}, r = - \frac{9 3 2 π ^{\frac{2}{3}}}{2 π} + i \frac{9 3 2 3 π ^{\frac{2}{3}}}{2 π}, r = - \frac{9 3 2 π ^{\frac{2}{3}}}{2 π} - i \frac{9 3 2 3 π ^{\frac{2}{3}}}{2 π}

Pasos de solución

972 = \frac{4}{6} π r^{3}

Intercambiar lados

\frac{4}{6} π r^{3} = 972

Simplificar

\frac{4}{6} π : \frac{2 π}{3}

\frac{2 π}{3} r^{3} = 972

Multiplicar ambos lados por

3

2 π r^{3} = 2916

Dividir ambos lados entre

2 π

r^{3} = \frac{1458}{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{1458}{π}, r = 3 \frac{1458}{π} \frac{- 1 + 3 i}{2}, r = 3 \frac{1458}{π} \frac{- 1 - 3 i}{2}

3 \frac{1458}{π} = \frac{9 3 2}{3 π}

Simplificar

3 \frac{1458}{π} \frac{- 1 + 3 i}{2} : - \frac{9 3 2 π ^{\frac{2}{3}}}{2 π} + i \frac{9 3 2 3 π ^{\frac{2}{3}}}{2 π}

Simplificar

3 \frac{1458}{π} \frac{- 1 - 3 i}{2} : - \frac{9 3 2 π ^{\frac{2}{3}}}{2 π} - i \frac{9 3 2 3 π ^{\frac{2}{3}}}{2 π}

r = \frac{9 3 2}{3 π}, r = - \frac{9 3 2 π ^{\frac{2}{3}}}{2 π} + i \frac{9 3 2 3 π ^{\frac{2}{3}}}{2 π}, r = - \frac{9 3 2 π ^{\frac{2}{3}}}{2 π} - i \frac{9 3 2 3 π ^{\frac{2}{3}}}{2 π}

6 (x^{2} - 3) - 2 x (3 x^{2} + 7) = 15 - 2 x

2 m^{3} + 12 m^{2} + 10 m = 0

(y^{2} - y - 30) (5 y - 40) = 0

144 x^{4} + 24 x^{2} + 1 = 0

77 = 16 \cdot (1 + r)^{4}