4z^5-10z^2=0

Lösung

4 z^{5} - 10 z^{2} = 0

z = 0, z = 3 \frac{5}{2}, z = - 3 \frac{5}{2} \frac{1}{2} + 3 \frac{5}{2} \frac{3}{2} i, z = - 3 \frac{5}{2} \frac{1}{2} - 3 \frac{5}{2} \frac{3}{2} i

Schritte zur Lösung

4 z^{5} - 10 z^{2} = 0

Faktorisiere

4 z^{5} - 10 z^{2} : 2 z^{2} (2 z^{3} - 5)

2 z^{2} (2 z^{3} - 5) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

z = 0 or 2 z^{3} - 5 = 0

Löse

2 z^{3} - 5 = 0 : z = 3 \frac{5}{2}, z = - 3 \frac{5}{2} \frac{1}{2} + 3 \frac{5}{2} \frac{3}{2} i, z = - 3 \frac{5}{2} \frac{1}{2} - 3 \frac{5}{2} \frac{3}{2} i

Die Lösungen sind

z = 0, z = 3 \frac{5}{2}, z = - 3 \frac{5}{2} \frac{1}{2} + 3 \frac{5}{2} \frac{3}{2} i, z = - 3 \frac{5}{2} \frac{1}{2} - 3 \frac{5}{2} \frac{3}{2} i

x^{8} + 2 x^{4} + 1 = 0

(x^{2} + x - 1) - x^{3} - 3 x = 2

r^{3} - 2 r^{2} + r = 0

so l v e f or y, x = 7 + (2 y + 1)^{3}

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