x^3+6x^2-81=0

Lösung

x^{3} + 6 x^{2} - 81 = 0

x = 3, x = - \frac{9}{2} + i \frac{3 3}{2}, x = - \frac{9}{2} - i \frac{3 3}{2}

Schritte zur Lösung

x^{3} + 6 x^{2} - 81 = 0

Faktorisiere

x^{3} + 6 x^{2} - 81 : (x - 3) (x^{2} + 9 x + 27)

(x - 3) (x^{2} + 9 x + 27) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 3 = 0 or x^{2} + 9 x + 27 = 0

Löse

x - 3 = 0 : x = 3

Löse

x^{2} + 9 x + 27 = 0 : x = - \frac{9}{2} + i \frac{3 3}{2}, x = - \frac{9}{2} - i \frac{3 3}{2}

Die Lösungen sind

x = 3, x = - \frac{9}{2} + i \frac{3 3}{2}, x = - \frac{9}{2} - i \frac{3 3}{2}

so l v e f or x, x^{3} + y^{3} = 18

so l v e f or x, x^{3} = \frac{y}{2}

x (1 - \frac{x ^{3}}{2000}) = 0

so l v e f or x, x^{3} + y^{3} = 36

x^{3} + 2 x - 9 x - 18 = 0