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Beliebt Algebra >

x^3-30x^2+15^3=0

Lösung

x^{3} - 30 x^{2} + 1 5^{3} = 0

Lösung

x = 15, x = \frac{15 + 15 5}{2}, x = \frac{15 - 15 5}{2}

+1

Dezimale

x = 15, x = 24.27050 \dots, x = - 9.27050 \dots

Schritte zur Lösung

x^{3} - 30 x^{2} + 1 5^{3} = 0

Schreibe

x^{3} - 30 x^{2} + 1 5^{3}

um:

x^{3} - 30 x^{2} + 3375

x^{3} - 30 x^{2} + 3375 = 0

Faktorisiere

x^{3} - 30 x^{2} + 3375 : (x - 15) (x^{2} - 15 x - 225)

(x - 15) (x^{2} - 15 x - 225) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 15 = 0 or x^{2} - 15 x - 225 = 0

Löse

x - 15 = 0 : x = 15

Löse

x^{2} - 15 x - 225 = 0 : x = \frac{15 + 15 5}{2}, x = \frac{15 - 15 5}{2}

Die Lösungen sind

x = 15, x = \frac{15 + 15 5}{2}, x = \frac{15 - 15 5}{2}

Graph

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