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Beliebt Algebra >

x^4-8x^2-9=0

Lösung

x^{4} - 8 x^{2} - 9 = 0

Lösung

x = 3, x = - 3, x = i, x = - i

Schritte zur Lösung

x^{4} - 8 x^{2} - 9 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - 8 u - 9 = 0

Löse

u^{2} - 8 u - 9 = 0 : u = 9, u = - 1

u = 9, u = - 1

Setze

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

löse für

x

Löse

x^{2} = 9 : x = 3, x = - 3

Löse

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

Die Lösungen sind

x = 3, x = - 3, x = i, x = - i

Graph

Beliebte Beispiele

(x^2-6x)^2+2*(x-3)^2=81

(x^{2} - 6 x)^{2} + 2 \cdot (x - 3)^{2} = 81

6 x^{7} - 8 = 2 (7 - 10)

(x^2-8)^2+x^2-8=20

(x^{2} - 8)^{2} + x^{2} - 8 = 20

x^3+7x^2+17x-24=0

x^{3} + 7 x^{2} + 17 x - 24 = 0

(x^2-1)(x^2-12)+24=0

(x^{2} - 1) (x^{2} - 12) + 24 = 0