-4y-(x^4+7x^2+10)y=0

Lösung

- 4 y - (x^{4} + 7 x^{2} + 10) y = 0

y = 0

Schritte zur Lösung

- 4 y - (x^{4} + 7 x^{2} + 10) y = 0

Faktorisiere

- 4 y - (x^{4} + 7 x^{2} + 10) y : - y (x^{4} + 7 x^{2} + 14)

- y (x^{4} + 7 x^{2} + 14) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

y = 0 or x^{4} + 7 x^{2} + 14 = 0

y = 0

Löse

x^{4} + 7 x^{2} + 14 = 0 : x = \frac{7}{2 7 + 2 14} + \frac{7 + 2 14}{2} i, x = - \frac{7}{2 ^{2} \cdot \frac{7 + 2 14}{2}} - \frac{7 + 2 14}{2} i, x = - \frac{7}{2 7 + 2 14} + \frac{7 + 2 14}{2} i, x = - \frac{7}{2 ( - 7 + 2 14 )} - \frac{7 + 2 14}{2} i

Die Lösungen sind

Entferne komplexe Lösungen

: x = \frac{7}{2 7 + 2 14} + \frac{7 + 2 14}{2} i, x = - \frac{7}{2 ^{2} \cdot \frac{7 + 2 14}{2}} - \frac{7 + 2 14}{2} i, x = - \frac{7}{2 7 + 2 14} + \frac{7 + 2 14}{2} i, x = - \frac{7}{2 ( - 7 + 2 14 )} - \frac{7 + 2 14}{2} i

y = 0

(x^{2} + 9) y^{1} + x y = 0

u \cdot v = 0

(x - 2) (y^{2} + 1) = 0

yz = 0

A \cdot B = 0