x^6-5x^3+6=0

Lösung

x^{6} - 5 x^{3} + 6 = 0

x = 33, x = - 33 \frac{1}{2} + 33 \frac{3}{2} i, x = - 33 \frac{1}{2} - 33 \frac{3}{2} i, x = 32, x = - 32 \frac{1}{2} + 32 \frac{3}{2} i, x = - 32 \frac{1}{2} - 32 \frac{3}{2} i

Schritte zur Lösung

x^{6} - 5 x^{3} + 6 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} - 5 u + 6 = 0

Löse

u^{2} - 5 u + 6 = 0 : u = 3, u = 2

u = 3, u = 2

Setze

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

löse für

x

Löse

x^{3} = 3 : x = 33, x = - 33 \frac{1}{2} + 33 \frac{3}{2} i, x = - 33 \frac{1}{2} - 33 \frac{3}{2} i

Löse

x^{3} = 2 : x = 32, x = - 32 \frac{1}{2} + 32 \frac{3}{2} i, x = - 32 \frac{1}{2} - 32 \frac{3}{2} i

Die Lösungen sind

x = 33, x = - 33 \frac{1}{2} + 33 \frac{3}{2} i, x = - 33 \frac{1}{2} - 33 \frac{3}{2} i, x = 32, x = - 32 \frac{1}{2} + 32 \frac{3}{2} i, x = - 32 \frac{1}{2} - 32 \frac{3}{2} i

x^{3} - 5 x^{2} + 2 x + 12 = 0

roo t s x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1

3 x^{3} + 7 x^{2} + 147 x + 343 = 0

z^{3} + 125 = 0

f a c t or x^{3} + x = 0