220000=100000*(1+x)^3

Lösung

220000 = 100000 \cdot (1 + x)^{3}

x = 3 \frac{11}{5} - 1, x = \frac{5 ^{\frac{2}{3}} ( - 3 11 - 2 3 5 )}{10} + i \frac{5 ^{\frac{2}{3}} 3 11 3}{10}, x = \frac{5 ^{\frac{2}{3}} ( - 3 11 - 2 3 5 )}{10} - i \frac{5 ^{\frac{2}{3}} 3 11 3}{10}

Schritte zur Lösung

220000 = 100000 (1 + x)^{3}

Tausche die Seiten

100000 (1 + x)^{3} = 220000

Teile beide Seiten durch

100000

(1 + x)^{3} = \frac{11}{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

1 + x = 3 \frac{11}{5} : x = 3 \frac{11}{5} - 1

Löse

1 + x = 3 \frac{11}{5} \frac{- 1 + 3 i}{2} : x = \frac{5 ^{\frac{2}{3}} ( - 3 11 - 2 3 5 )}{10} + i \frac{5 ^{\frac{2}{3}} 3 11 3}{10}

Löse

1 + x = 3 \frac{11}{5} \frac{- 1 - 3 i}{2} : x = \frac{5 ^{\frac{2}{3}} ( - 3 11 - 2 3 5 )}{10} - i \frac{5 ^{\frac{2}{3}} 3 11 3}{10}

Die Lösungen sind

x = 3 \frac{11}{5} - 1, x = \frac{5 ^{\frac{2}{3}} ( - 3 11 - 2 3 5 )}{10} + i \frac{5 ^{\frac{2}{3}} 3 11 3}{10}, x = \frac{5 ^{\frac{2}{3}} ( - 3 11 - 2 3 5 )}{10} - i \frac{5 ^{\frac{2}{3}} 3 11 3}{10}

so l v e f or x, f = 10 + x^{3} f (27)

(x - 2)^{4} (x + 1) (x + 4) = 0

(3 x - 2)^{3} = (2 - 3 x)^{2}

so l v e f or x, a = (2 x^{5} y^{3})^{3}

a^{3} + 12 a - 6.5 = 0