5(x-1)^3=18

Lösung

5 (x - 1)^{3} = 18

x = 3 \frac{18}{5} + 1, x = \frac{5 ^{\frac{2}{3}} 3 2 ( - 3 9 + 2 ^{\frac{2}{3}} 3 5 )}{10} + i \frac{5 ^{\frac{2}{3}} 3 18 3}{10}, x = \frac{5 ^{\frac{2}{3}} 3 2 ( - 3 9 + 2 ^{\frac{2}{3}} 3 5 )}{10} - i \frac{5 ^{\frac{2}{3}} 3 18 3}{10}

Schritte zur Lösung

5 (x - 1)^{3} = 18

Teile beide Seiten durch

5

(x - 1)^{3} = \frac{18}{5}

Für

g^{3} (x) = f (a)

sind die Lösungen

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

Löse

x - 1 = 3 \frac{18}{5} : x = 3 \frac{18}{5} + 1

Löse

x - 1 = 3 \frac{18}{5} \frac{- 1 + 3 i}{2} : x = \frac{5 ^{\frac{2}{3}} 3 2 ( - 3 9 + 2 ^{\frac{2}{3}} 3 5 )}{10} + i \frac{5 ^{\frac{2}{3}} 3 18 3}{10}

Löse

x - 1 = 3 \frac{18}{5} \frac{- 1 - 3 i}{2} : x = \frac{5 ^{\frac{2}{3}} 3 2 ( - 3 9 + 2 ^{\frac{2}{3}} 3 5 )}{10} - i \frac{5 ^{\frac{2}{3}} 3 18 3}{10}

Die Lösungen sind

x = 3 \frac{18}{5} + 1, x = \frac{5 ^{\frac{2}{3}} 3 2 ( - 3 9 + 2 ^{\frac{2}{3}} 3 5 )}{10} + i \frac{5 ^{\frac{2}{3}} 3 18 3}{10}, x = \frac{5 ^{\frac{2}{3}} 3 2 ( - 3 9 + 2 ^{\frac{2}{3}} 3 5 )}{10} - i \frac{5 ^{\frac{2}{3}} 3 18 3}{10}

- x^{3} + 3 x^{2} + 18 x = 0

4 x^{4} - 3 = 2 x + 1

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

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

x^{3} + 4 x^{2} - 9 x - 36 = 0