8x^3-12x^2+6x-65=0

Lösung

8 x^{3} - 12 x^{2} + 6 x - 65 = 0

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

Schritte zur Lösung

8 x^{3} - 12 x^{2} + 6 x - 65 = 0

Faktorisiere

8 x^{3} - 12 x^{2} + 6 x - 65 : (2 x - 5) (4 x^{2} + 4 x + 13)

(2 x - 5) (4 x^{2} + 4 x + 13) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

2 x - 5 = 0 or 4 x^{2} + 4 x + 13 = 0

Löse

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

Löse

4 x^{2} + 4 x + 13 = 0 : x = - \frac{1}{2} + 3 i, x = - \frac{1}{2} - 3 i

Die Lösungen sind

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

2 x^{1} + x^{2} - x^{3} + x^{4} = - 2

x^{3} = 5 x^{2} - 6 x

(3 p + 7) (3 p - 7) (p + 8) = 0

x \cdot (2 x - 4)^{2} = 0

so l v e f or x, 3 x^{3} + x^{2} - 8 x + 4 = 0