x^6+13x^3+30=0

Lösung

x^{6} + 13 x^{3} + 30 = 0

x = - 33, x = \frac{3 3}{2} - \frac{6 3 ^{5}}{2} i, x = \frac{3 3}{2} + \frac{6 3 ^{5}}{2} i, x = - 310, x = - \frac{3 5 ( - 1 + 3 i )}{3 2 ^{2}}, x = - \frac{3 5 ( - 1 - 3 i )}{3 2 ^{2}}

Schritte zur Lösung

x^{6} + 13 x^{3} + 30 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} + 13 u + 30 = 0

Löse

u^{2} + 13 u + 30 = 0 : u = - 3, u = - 10

u = - 3, u = - 10

Setze

u = x^{3} w i e d er e in,

löse für

x

Löse

x^{3} = - 3 : x = - 33, x = \frac{3 3}{2} - \frac{6 3 ^{5}}{2} i, x = \frac{3 3}{2} + \frac{6 3 ^{5}}{2} i

Löse

x^{3} = - 10 : x = - 310, x = - \frac{3 5 ( - 1 + 3 i )}{3 2 ^{2}}, x = - \frac{3 5 ( - 1 - 3 i )}{3 2 ^{2}}

Die Lösungen sind

x = - 33, x = \frac{3 3}{2} - \frac{6 3 ^{5}}{2} i, x = \frac{3 3}{2} + \frac{6 3 ^{5}}{2} i, x = - 310, x = - \frac{3 5 ( - 1 + 3 i )}{3 2 ^{2}}, x = - \frac{3 5 ( - 1 - 3 i )}{3 2 ^{2}}

(x) (1.06) (70000 - x) (1.085) = 70000 + 5000

- x > - 4

s im pl i f y \frac{x}{y} + \frac{y}{x}

f a c t or 2 x^{3} - 6 x^{2} + 4 x

s im pl i f y 0.0901 (\frac{1}{1000})