10x^3=(4/3)pia^3

Lösung

10 x^{3} = (\frac{4}{3}) π a^{3}

x = 3 \frac{2 π a ^{3}}{15}, x = - \frac{1 5 ^{\frac{2}{3}} 3 2 3 π a}{30} + i \frac{5 ^{\frac{2}{3}} 3 2 6 3 3 π a}{10}, x = - \frac{1 5 ^{\frac{2}{3}} 3 2 3 π a}{30} - i \frac{5 ^{\frac{2}{3}} 3 2 6 3 3 π a}{10}

Schritte zur Lösung

10 x^{3} = (\frac{4}{3}) π a^{3}

Teile beide Seiten durch

10

x^{3} = \frac{2 π a ^{3}}{15}

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}

x = 3 \frac{2 π a ^{3}}{15}, x = 3 \frac{2 π a ^{3}}{15} \frac{- 1 + 3 i}{2}, x = 3 \frac{2 π a ^{3}}{15} \frac{- 1 - 3 i}{2}

Vereinfache

3 \frac{2 π a ^{3}}{15} \frac{- 1 + 3 i}{2} : - \frac{1 5 ^{\frac{2}{3}} 3 2 3 π a}{30} + i \frac{5 ^{\frac{2}{3}} 3 2 6 3 3 π a}{10}

Vereinfache

3 \frac{2 π a ^{3}}{15} \frac{- 1 - 3 i}{2} : - \frac{1 5 ^{\frac{2}{3}} 3 2 3 π a}{30} - i \frac{5 ^{\frac{2}{3}} 3 2 6 3 3 π a}{10}

x = 3 \frac{2 π a ^{3}}{15}, x = - \frac{1 5 ^{\frac{2}{3}} 3 2 3 π a}{30} + i \frac{5 ^{\frac{2}{3}} 3 2 6 3 3 π a}{10}, x = - \frac{1 5 ^{\frac{2}{3}} 3 2 3 π a}{30} - i \frac{5 ^{\frac{2}{3}} 3 2 6 3 3 π a}{10}

x^{4} - 28 x^{3} + 288 x^{2} - 1116 x + 1296 = 0

2 x^{3} - 3 x^{2} - 12 x + 3 = 0

x^{3} + 6 x^{2} + 12 x + 7 = 0

x^{3} + x^{2} - 12 = 0

x^{4} + 4 x^{3} - 1 = 0