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Beliebt Algebra >

-20x^3+216x^2-648x+432=0

Lösung

- 20 x^{3} + 216 x^{2} - 648 x + 432 = 0

Lösung

x = 6, x = \frac{3 ( 4 + 6 )}{5}, x = \frac{3 ( 4 - 6 )}{5}

+1

Dezimale

x = 6, x = 3.86969 \dots, x = 0.93030 \dots

Schritte zur Lösung

- 20 x^{3} + 216 x^{2} - 648 x + 432 = 0

Faktorisiere

- 20 x^{3} + 216 x^{2} - 648 x + 432 : - 4 (x - 6) (5 x^{2} - 24 x + 18)

- 4 (x - 6) (5 x^{2} - 24 x + 18) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 6 = 0 or 5 x^{2} - 24 x + 18 = 0

Löse

x - 6 = 0 : x = 6

Löse

5 x^{2} - 24 x + 18 = 0 : x = \frac{3 ( 4 + 6 )}{5}, x = \frac{3 ( 4 - 6 )}{5}

Die Lösungen sind

x = 6, x = \frac{3 ( 4 + 6 )}{5}, x = \frac{3 ( 4 - 6 )}{5}

Graph

Beliebte Beispiele

x^3-9x^2+26x+22=0

x^{3} - 9 x^{2} + 26 x + 22 = 0

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- x^{3} + 13 x^{2} - 40 x + 36 = 0

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

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

x^{3} - x^{2} - 4 x - 4 = 0