faktorisieren x^3-8x^2+22x-21=0

Lösung

faktorisieren

x^{3} - 8 x^{2} + 22 x - 21 = 0

x = 3, x = \frac{5}{2} + i \frac{3}{2}, x = \frac{5}{2} - i \frac{3}{2}

Schritte zur Lösung

x^{3} - 8 x^{2} + 22 x - 21 = 0

Faktorisiere

x^{3} - 8 x^{2} + 22 x - 21 : (x - 3) (x^{2} - 5 x + 7)

(x - 3) (x^{2} - 5 x + 7) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 3 = 0 or x^{2} - 5 x + 7 = 0

Löse

x - 3 = 0 : x = 3

Löse

x^{2} - 5 x + 7 = 0 : x = \frac{5}{2} + i \frac{3}{2}, x = \frac{5}{2} - i \frac{3}{2}

Die Lösungen sind

x = 3, x = \frac{5}{2} + i \frac{3}{2}, x = \frac{5}{2} - i \frac{3}{2}

so l v e f or y, x^{4} + y^{4} = 0

f a c t or m^{3} + 3 m^{2} - 4 = 0

3 x^{3} - 17 x^{2} + 18 x + 8 = 0

so l v e f or f, f x = 4 x^{3} - 6 x^{2}

roo t s x^{4} - 81