(x^3)/2 =125

Lösung

\frac{x ^{3}}{2} = 125

x = 532, x = \frac{5 ( - 1 + 3 i )}{3 2 ^{2}}, x = \frac{5 ( - 1 - 3 i )}{3 2 ^{2}}

Schritte zur Lösung

\frac{x ^{3}}{2} = 125

Multipliziere beide Seiten mit

2

x^{3} = 250

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 = 3250, x = 3250 \frac{- 1 + 3 i}{2}, x = 3250 \frac{- 1 - 3 i}{2}

3250 = 532

Vereinfache

3250 \frac{- 1 + 3 i}{2} : \frac{5 ( - 1 + 3 i )}{3 2 ^{2}}

Vereinfache

3250 \frac{- 1 - 3 i}{2} : \frac{5 ( - 1 - 3 i )}{3 2 ^{2}}

x = 532, x = \frac{5 ( - 1 + 3 i )}{3 2 ^{2}}, x = \frac{5 ( - 1 - 3 i )}{3 2 ^{2}}

(x - a)^{2} (x + a + 1)^{3} = 0

(x + 1)^{2} - (x - 1)^{3} = 6 x (x - 3)

- 54 x^{3} - 54 x^{2} - 18 x - 5 = 0

c^{3} = 216

x^{4} + 4 x^{3} + 5 x^{2} + 2 = 0