82853.3352= 4/3 pir^3

Lösung

82853.3352 = \frac{4}{3} π r^{3}

r = 3 \frac{248560.0056}{4 π}, r = - \frac{4 ^{\frac{2}{3}} 3 248560.0056 π ^{\frac{2}{3}}}{8 π} + i \frac{4 ^{\frac{2}{3}} 3 3 248560.0056 π ^{\frac{2}{3}}}{8 π}, r = - \frac{4 ^{\frac{2}{3}} 3 248560.0056 π ^{\frac{2}{3}}}{8 π} - i \frac{4 ^{\frac{2}{3}} 3 3 248560.0056 π ^{\frac{2}{3}}}{8 π}

Schritte zur Lösung

82853.3352 = \frac{4}{3} π r^{3}

Tausche die Seiten

\frac{4}{3} π r^{3} = 82853.3352

Vereinfache

\frac{4}{3} π : \frac{4 π}{3}

\frac{4 π}{3} r^{3} = 82853.3352

Multipliziere beide Seiten mit

3

4 π r^{3} = 248560.0056

Teile beide Seiten durch

4 π

r^{3} = \frac{248560.0056}{4 π}

Für

x^{3} = f (a)

sind die Lösungen

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

r = 3 \frac{248560.0056}{4 π}, r = 3 \frac{248560.0056}{4 π} \frac{- 1 + 3 i}{2}, r = 3 \frac{248560.0056}{4 π} \frac{- 1 - 3 i}{2}

Vereinfache

3 \frac{248560.0056}{4 π} \frac{- 1 + 3 i}{2} : - \frac{4 ^{\frac{2}{3}} 3 248560.0056 π ^{\frac{2}{3}}}{8 π} + i \frac{4 ^{\frac{2}{3}} 3 3 248560.0056 π ^{\frac{2}{3}}}{8 π}

Vereinfache

3 \frac{248560.0056}{4 π} \frac{- 1 - 3 i}{2} : - \frac{4 ^{\frac{2}{3}} 3 248560.0056 π ^{\frac{2}{3}}}{8 π} - i \frac{4 ^{\frac{2}{3}} 3 3 248560.0056 π ^{\frac{2}{3}}}{8 π}

r = 3 \frac{248560.0056}{4 π}, r = - \frac{4 ^{\frac{2}{3}} 3 248560.0056 π ^{\frac{2}{3}}}{8 π} + i \frac{4 ^{\frac{2}{3}} 3 3 248560.0056 π ^{\frac{2}{3}}}{8 π}, r = - \frac{4 ^{\frac{2}{3}} 3 248560.0056 π ^{\frac{2}{3}}}{8 π} - i \frac{4 ^{\frac{2}{3}} 3 3 248560.0056 π ^{\frac{2}{3}}}{8 π}

x^{3} + 3 x^{2} + 3 x - 8059 = 0

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

x^{3} - 27 x = - 10

9 m^{5} = 27 m^{3}

x^{3} - 4 x^{2} - 8 x - 10 = 0