2= 4/3 pir^3

Lösung

2 = \frac{4}{3} π r^{3}

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

Schritte zur Lösung

2 = \frac{4}{3} π r^{3}

Tausche die Seiten

\frac{4}{3} π r^{3} = 2

Vereinfache

\frac{4}{3} π : \frac{4 π}{3}

\frac{4 π}{3} r^{3} = 2

Multipliziere beide Seiten mit

3

4 π r^{3} = 6

Teile beide Seiten durch

4 π

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

Vereinfache

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

Vereinfache

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

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

1500 = 986 (1 + x)^{3}

x^{6} + 2 x^{3} + 2 = 0

x^{4} - 3 x^{3} - 5 x^{2} + 13 x + 6 = 0

x^{6} + 2 x^{3} - 3 = 0

4 x^{3} + 30 x^{2} + 70 x + 50 = 0