216x^3(x-1)^3=64x^6

Lösung

216 x^{3} (x - 1)^{3} = 64 x^{6}

x = 0, x = 3, x = \frac{12}{19} + i \frac{3 3}{19}, x = \frac{12}{19} - i \frac{3 3}{19}

Schritte zur Lösung

216 x^{3} (x - 1)^{3} = 64 x^{6}

Verschiebe

64 x^{6}

auf die linke Seite

216 x^{3} (x - 1)^{3} - 64 x^{6} = 0

Faktorisiere

216 x^{3} (x - 1)^{3} - 64 x^{6} : 8 x^{3} (x - 3) (19 x^{2} - 24 x + 9)

8 x^{3} (x - 3) (19 x^{2} - 24 x + 9) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x - 3 = 0 or 19 x^{2} - 24 x + 9 = 0

Löse

x - 3 = 0 : x = 3

Löse

19 x^{2} - 24 x + 9 = 0 : x = \frac{12}{19} + i \frac{3 3}{19}, x = \frac{12}{19} - i \frac{3 3}{19}

Die Lösungen sind

x = 0, x = 3, x = \frac{12}{19} + i \frac{3 3}{19}, x = \frac{12}{19} - i \frac{3 3}{19}

3 (5 x + 2) (x^{2} - 81) = 0

2 x^{3} - 16 x^{2} - 18 x = 0

27 x^{3} = (x + 5)^{3}

8 x^{3} - 12 x^{2} + 2 x - 3 = 0

(x - 2)^{3} - 5 = 0