23305=7000(1+x)^3

Lösung

23305 = 7000 (1 + x)^{3}

x = \frac{3 4661}{2 3 175} - 1, x = \frac{7 ^{\frac{2}{3}} 3 5 ( - 3 4661 - 4 \cdot 5 ^{\frac{2}{3}} 3 7 )}{140} + i \frac{7 ^{\frac{2}{3}} 3 23305 3}{140}, x = \frac{7 ^{\frac{2}{3}} 3 5 ( - 3 4661 - 4 \cdot 5 ^{\frac{2}{3}} 3 7 )}{140} - i \frac{7 ^{\frac{2}{3}} 3 23305 3}{140}

Schritte zur Lösung

23305 = 7000 (1 + x)^{3}

Tausche die Seiten

7000 (1 + x)^{3} = 23305

Teile beide Seiten durch

7000

(1 + x)^{3} = \frac{4661}{1400}

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{4661}{1400} : x = \frac{3 4661}{2 3 175} - 1

Löse

1 + x = 3 \frac{4661}{1400} \frac{- 1 + 3 i}{2} : x = \frac{7 ^{\frac{2}{3}} 3 5 ( - 3 4661 - 4 \cdot 5 ^{\frac{2}{3}} 3 7 )}{140} + i \frac{7 ^{\frac{2}{3}} 3 23305 3}{140}

Löse

1 + x = 3 \frac{4661}{1400} \frac{- 1 - 3 i}{2} : x = \frac{7 ^{\frac{2}{3}} 3 5 ( - 3 4661 - 4 \cdot 5 ^{\frac{2}{3}} 3 7 )}{140} - i \frac{7 ^{\frac{2}{3}} 3 23305 3}{140}

Die Lösungen sind

x = \frac{3 4661}{2 3 175} - 1, x = \frac{7 ^{\frac{2}{3}} 3 5 ( - 3 4661 - 4 \cdot 5 ^{\frac{2}{3}} 3 7 )}{140} + i \frac{7 ^{\frac{2}{3}} 3 23305 3}{140}, x = \frac{7 ^{\frac{2}{3}} 3 5 ( - 3 4661 - 4 \cdot 5 ^{\frac{2}{3}} 3 7 )}{140} - i \frac{7 ^{\frac{2}{3}} 3 23305 3}{140}

(6 x^{2} - x - 2) (a x + 9) = 0, a \neq = 0

16 x^{3} + 64 x^{2} - 25 x - 100 = 0

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

(x - 3)^{4} - 30 = 0

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