-3x^4+4x^2+8x+4=0

Lösung

- 3 x^{4} + 4 x^{2} + 8 x + 4 = 0

x = i \frac{2 3 y _{100}}{3}, x = - i \frac{2 3 y _{100}}{3}, x = \frac{2 y _{100}}{3}, x = - \frac{2 y _{100}}{3}

Schritte zur Lösung

- 3 x^{4} + 4 x^{2} + 8 x + 4 = 0

Faktorisiere

- 3 x^{4} + 4 x^{2} + 8 x + 4 : - (3 x^{2} + 2 y_{100}) (3 x^{2} - 2 y_{100})

- (3 x^{2} + 2 y_{100}) (3 x^{2} - 2 y_{100}) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

3 x^{2} + 2 y_{100} = 0 or 3 x^{2} - 2 y_{100} = 0

Löse

3 x^{2} + 2 y_{100} = 0 : x = i \frac{2 3 y _{100}}{3}, x = - i \frac{2 3 y _{100}}{3}

Löse

3 x^{2} - 2 y_{100} = 0 : x = \frac{2 y _{100}}{3}, x = - \frac{2 y _{100}}{3}

Die Lösungen sind

x = i \frac{2 3 y _{100}}{3}, x = - i \frac{2 3 y _{100}}{3}, x = \frac{2 y _{100}}{3}, x = - \frac{2 y _{100}}{3}

1031 = x^{5} + x + 3

2 x^{4} - 3 x^{2} + 1 = 0

so l v e f or x, 0 = x^{3} - y + 5

2 x^{3} - 5 x^{2} = 12 x

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