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Beliebt Algebra >

(x-2)(x-1)(x)=3360

Lösung

(x - 2) (x - 1) (x) = 3360

Lösung

x = 16, x = - \frac{13}{2} + i \frac{671}{2}, x = - \frac{13}{2} - i \frac{671}{2}

Schritte zur Lösung

(x - 2) (x - 1) (x) = 3360

Schreibe

(x - 2) (x - 1) (x)

um:

x^{3} - 3 x^{2} + 2 x

x^{3} - 3 x^{2} + 2 x = 3360

Verschiebe

3360

auf die linke Seite

x^{3} - 3 x^{2} + 2 x - 3360 = 0

Faktorisiere

x^{3} - 3 x^{2} + 2 x - 3360 : (x - 16) (x^{2} + 13 x + 210)

(x - 16) (x^{2} + 13 x + 210) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 16 = 0 or x^{2} + 13 x + 210 = 0

Löse

x - 16 = 0 : x = 16

Löse

x^{2} + 13 x + 210 = 0 : x = - \frac{13}{2} + i \frac{671}{2}, x = - \frac{13}{2} - i \frac{671}{2}

Die Lösungen sind

x = 16, x = - \frac{13}{2} + i \frac{671}{2}, x = - \frac{13}{2} - i \frac{671}{2}

Graph

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