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Beliebt Algebra >

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

Lösung

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

Lösung

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

Schreibe die Gleichung um mit

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

und

u^{4} = x^{8}

u^{4} + 2 u^{2} + 1 = 0

Löse

u^{4} + 2 u^{2} + 1 = 0 : u = i, u = - i

u = i, u = - i

Setze

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

löse für

x

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 = \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^2+x-1)-x^3-3x=2

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

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

solvefor y,x=7+(2y+1)^3

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

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

6 x^{5} - 6 x^{4} = 0