x^3-x^2-75/8 =0

Lösung

x^{3} - x^{2} - \frac{75}{8} = 0

x = \frac{5}{2}, x = - \frac{3}{4} + i \frac{51}{4}, x = - \frac{3}{4} - i \frac{51}{4}

Schritte zur Lösung

x^{3} - x^{2} - \frac{75}{8} = 0

Multipliziere beide Seiten mit

8

8 x^{3} - 8 x^{2} - 75 = 0

Faktorisiere

8 x^{3} - 8 x^{2} - 75 : (2 x - 5) (4 x^{2} + 6 x + 15)

(2 x - 5) (4 x^{2} + 6 x + 15) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

2 x - 5 = 0 or 4 x^{2} + 6 x + 15 = 0

Löse

2 x - 5 = 0 : x = \frac{5}{2}

Löse

4 x^{2} + 6 x + 15 = 0 : x = - \frac{3}{4} + i \frac{51}{4}, x = - \frac{3}{4} - i \frac{51}{4}

Die Lösungen sind

x = \frac{5}{2}, x = - \frac{3}{4} + i \frac{51}{4}, x = - \frac{3}{4} - i \frac{51}{4}

1400 = 1000 \cdot (1 + x)^{3}

2 x^{3} - 5 x^{2} - 5 x - 1 = 0

2 x^{5} - 5 x^{4} + 10 x^{2} - 10 x + 1 = 0

x \cdot x \cdot x = 0.5

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