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Beliebt Algebra >

x^6+x^4+x^2+1=0

Lösung

x^{6} + x^{4} + x^{2} + 1 = 0

Lösung

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

Schritte zur Lösung

x^{6} + x^{4} + x^{2} + 1 = 0

Schreibe die Gleichung um mit

u = x^{2}, u^{2} = x^{4}

und

u^{3} = x^{6}

u^{3} + u^{2} + u + 1 = 0

Löse

u^{3} + u^{2} + u + 1 = 0 : u = - 1, u = i, u = - i

u = - 1, u = i, u = - i

Setze

u = x^{2} w i e d er e in,

löse für

x

Löse

x^{2} = - 1 : x = i, x = - i

Löse

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

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

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

56 x^{6} - 336 x^{5} = 0

5 x^{5} - 80 x = 0

wurzeln von r^3-7r^2+16r-12

roo t s r^{3} - 7 r^{2} + 16 r - 12

6x^4+5x^3+25x^2+20x+4=0

6 x^{4} + 5 x^{3} + 25 x^{2} + 20 x + 4 = 0