473=(7pik^3)/(48)

Lösung

473 = \frac{7 π k ^{3}}{48}

k = \frac{2 3 2838}{3 7 3 π}, k = - \frac{7 ^{\frac{2}{3}} 3 2838 π ^{\frac{2}{3}}}{7 π} + i \frac{3 ^{\frac{5}{6}} \cdot 7 ^{\frac{2}{3}} 3 946 π ^{\frac{2}{3}}}{7 π}, k = - \frac{7 ^{\frac{2}{3}} 3 2838 π ^{\frac{2}{3}}}{7 π} - i \frac{3 ^{\frac{5}{6}} \cdot 7 ^{\frac{2}{3}} 3 946 π ^{\frac{2}{3}}}{7 π}

Schritte zur Lösung

473 = \frac{7 π k ^{3}}{48}

Tausche die Seiten

\frac{7 π k ^{3}}{48} = 473

Multipliziere beide Seiten mit

48

7 π k^{3} = 22704

Teile beide Seiten durch

7 π

k^{3} = \frac{22704}{7 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}

k = 3 \frac{22704}{7 π}, k = 3 \frac{22704}{7 π} \frac{- 1 + 3 i}{2}, k = 3 \frac{22704}{7 π} \frac{- 1 - 3 i}{2}

3 \frac{22704}{7 π} = \frac{2 3 2838}{3 7 3 π}

Vereinfache

3 \frac{22704}{7 π} \frac{- 1 + 3 i}{2} : - \frac{7 ^{\frac{2}{3}} 3 2838 π ^{\frac{2}{3}}}{7 π} + i \frac{3 ^{\frac{5}{6}} \cdot 7 ^{\frac{2}{3}} 3 946 π ^{\frac{2}{3}}}{7 π}

Vereinfache

3 \frac{22704}{7 π} \frac{- 1 - 3 i}{2} : - \frac{7 ^{\frac{2}{3}} 3 2838 π ^{\frac{2}{3}}}{7 π} - i \frac{3 ^{\frac{5}{6}} \cdot 7 ^{\frac{2}{3}} 3 946 π ^{\frac{2}{3}}}{7 π}

k = \frac{2 3 2838}{3 7 3 π}, k = - \frac{7 ^{\frac{2}{3}} 3 2838 π ^{\frac{2}{3}}}{7 π} + i \frac{3 ^{\frac{5}{6}} \cdot 7 ^{\frac{2}{3}} 3 946 π ^{\frac{2}{3}}}{7 π}, k = - \frac{7 ^{\frac{2}{3}} 3 2838 π ^{\frac{2}{3}}}{7 π} - i \frac{3 ^{\frac{5}{6}} \cdot 7 ^{\frac{2}{3}} 3 946 π ^{\frac{2}{3}}}{7 π}

y^{4} = 2

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

- a^{3} + 2 a^{2} + 3 a + 2 = 0

0 = x^{3} - 6 x^{2} + 11 x - 6

s^{3} + 12 s^{2} + 20 s = 0