x^6-22x^3+49=0

Lösung

x^{6} - 22 x^{3} + 49 = 0

x = 3 11 + 62, x = - 3 11 + 62 \frac{1}{2} + 3 11 + 62 \frac{3}{2} i, x = - 3 11 + 62 \frac{1}{2} - 3 11 + 62 \frac{3}{2} i, x = 3 11 - 62, x = - 3 11 - 62 \frac{1}{2} + 3 11 - 62 \frac{3}{2} i, x = - 3 11 - 62 \frac{1}{2} - 3 11 - 62 \frac{3}{2} i

Schritte zur Lösung

x^{6} - 22 x^{3} + 49 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} - 22 u + 49 = 0

Löse

u^{2} - 22 u + 49 = 0 : u = 11 + 62, u = 11 - 62

u = 11 + 62, u = 11 - 62

Setze

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

löse für

x

Löse

x^{3} = 11 + 62 : x = 3 11 + 62, x = - 3 11 + 62 \frac{1}{2} + 3 11 + 62 \frac{3}{2} i, x = - 3 11 + 62 \frac{1}{2} - 3 11 + 62 \frac{3}{2} i

Löse

x^{3} = 11 - 62 : x = 3 11 - 62, x = - 3 11 - 62 \frac{1}{2} + 3 11 - 62 \frac{3}{2} i, x = - 3 11 - 62 \frac{1}{2} - 3 11 - 62 \frac{3}{2} i

Die Lösungen sind

x = 3 11 + 62, x = - 3 11 + 62 \frac{1}{2} + 3 11 + 62 \frac{3}{2} i, x = - 3 11 + 62 \frac{1}{2} - 3 11 + 62 \frac{3}{2} i, x = 3 11 - 62, x = - 3 11 - 62 \frac{1}{2} + 3 11 - 62 \frac{3}{2} i, x = - 3 11 - 62 \frac{1}{2} - 3 11 - 62 \frac{3}{2} i

5 x^{3} - 125 x^{5} = 0

(x^{2} + x)^{2} = 5 x^{2} + 5 x - 6

lo g_{2} (256) = \frac{x ^{3}}{8}

4 x^{4} - 10 x^{3} - 1 x^{2} = 0

3 x^{4} - 8 x^{3} - 16 x^{2} + 24 x + 32 = 0