-32x^5+160x^3-120x=0

Lösung

- 32 x^{5} + 160 x^{3} - 120 x = 0

x = 0, x = \frac{5 + 10}{2}, x = - \frac{5 + 10}{2}, x = \frac{5 - 10}{2}, x = - \frac{5 - 10}{2}

Dezimale

x = 0, x = 2.02018 \dots, x = - 2.02018 \dots, x = 0.95857 \dots, x = - 0.95857 \dots

Schritte zur Lösung

- 32 x^{5} + 160 x^{3} - 120 x = 0

Faktorisiere

- 32 x^{5} + 160 x^{3} - 120 x : - 8 x (4 x^{4} - 20 x^{2} + 15)

- 8 x (4 x^{4} - 20 x^{2} + 15) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or 4 x^{4} - 20 x^{2} + 15 = 0

Löse

4 x^{4} - 20 x^{2} + 15 = 0 : x = \frac{5 + 10}{2}, x = - \frac{5 + 10}{2}, x = \frac{5 - 10}{2}, x = - \frac{5 - 10}{2}

Die Lösungen sind

x = 0, x = \frac{5 + 10}{2}, x = - \frac{5 + 10}{2}, x = \frac{5 - 10}{2}, x = - \frac{5 - 10}{2}

s^{4} - 10 s^{3} - 5 s^{2} = 0

v^{10} - 6 v = - 104

6 x^{5} + 20 x^{3} = 23 x^{4}

x^{7} + 1 = 0

x^{6} + 9 x^{3} - 5 = 0