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Beliebt Algebra >

x^3-12x^2+48x-63=0

Lösung

x^{3} - 12 x^{2} + 48 x - 63 = 0

Lösung

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

Schritte zur Lösung

x^{3} - 12 x^{2} + 48 x - 63 = 0

Faktorisiere

x^{3} - 12 x^{2} + 48 x - 63 : (x - 3) (x^{2} - 9 x + 21)

(x - 3) (x^{2} - 9 x + 21) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 3 = 0 or x^{2} - 9 x + 21 = 0

Löse

x - 3 = 0 : x = 3

Löse

x^{2} - 9 x + 21 = 0 : x = \frac{9}{2} + i \frac{3}{2}, x = \frac{9}{2} - i \frac{3}{2}

Die Lösungen sind

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

Graph

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