5000=4000(1+x)^3

Lösung

5000 = 4000 (1 + x)^{3}

x = 3 \frac{5}{4} - 1, x = \frac{- 8 - 4 ^{\frac{2}{3}} 3 5}{8} + i \frac{4 ^{\frac{2}{3}} 3 5 3}{8}, x = \frac{- 8 - 4 ^{\frac{2}{3}} 3 5}{8} - i \frac{4 ^{\frac{2}{3}} 3 5 3}{8}

Schritte zur Lösung

5000 = 4000 (1 + x)^{3}

Tausche die Seiten

4000 (1 + x)^{3} = 5000

Teile beide Seiten durch

4000

(1 + x)^{3} = \frac{5}{4}

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

1 + x = 3 \frac{5}{4} : x = 3 \frac{5}{4} - 1

Löse

1 + x = 3 \frac{5}{4} \frac{- 1 + 3 i}{2} : x = \frac{- 8 - 4 ^{\frac{2}{3}} 3 5}{8} + i \frac{4 ^{\frac{2}{3}} 3 5 3}{8}

Löse

1 + x = 3 \frac{5}{4} \frac{- 1 - 3 i}{2} : x = \frac{- 8 - 4 ^{\frac{2}{3}} 3 5}{8} - i \frac{4 ^{\frac{2}{3}} 3 5 3}{8}

Die Lösungen sind

x = 3 \frac{5}{4} - 1, x = \frac{- 8 - 4 ^{\frac{2}{3}} 3 5}{8} + i \frac{4 ^{\frac{2}{3}} 3 5 3}{8}, x = \frac{- 8 - 4 ^{\frac{2}{3}} 3 5}{8} - i \frac{4 ^{\frac{2}{3}} 3 5 3}{8}

220 x^{3} - 48 x^{2} = 0

so l v e f or x, y^{2} = k x^{3}

roo t s x^{6} - 64

x^{3} + 7 x^{2} + 4 x - 12 = 0

x^{5} - 5 x^{3} = 36 x