125x^3+150x^2+60x=0

Lösung

125 x^{3} + 150 x^{2} + 60 x = 0

x = 0, x = - \frac{3}{5} + i \frac{3}{5}, x = - \frac{3}{5} - i \frac{3}{5}

Schritte zur Lösung

125 x^{3} + 150 x^{2} + 60 x = 0

Faktorisiere

125 x^{3} + 150 x^{2} + 60 x : 5 x (25 x^{2} + 30 x + 12)

5 x (25 x^{2} + 30 x + 12) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or 25 x^{2} + 30 x + 12 = 0

Löse

25 x^{2} + 30 x + 12 = 0 : x = - \frac{3}{5} + i \frac{3}{5}, x = - \frac{3}{5} - i \frac{3}{5}

Die Lösungen sind

x = 0, x = - \frac{3}{5} + i \frac{3}{5}, x = - \frac{3}{5} - i \frac{3}{5}

[(2 - x) \cdot (5 - 6 + 3)]^{3} x [(2 - 3) + (6 - 7 - 1)^{2}] = - 192

x^{22} x - 8 = 0

so l v e f or y, (x^{2} + y^{2} + a x)^{2} = a^{2} (x^{2} + y^{2})

x^{3} + 24 x + 16 = 0

x^{3} = 38 + 175