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Beliebt Algebra >

(x^2+3)^2-19(x^2+3)+84=0

Lösung

(x^{2} + 3)^{2} - 19 (x^{2} + 3) + 84 = 0

Lösung

x = 3, x = - 3, x = 2, x = - 2

Schritte zur Lösung

(x^{2} + 3)^{2} - 19 (x^{2} + 3) + 84 = 0

Schreibe

(x^{2} + 3)^{2} - 19 (x^{2} + 3) + 84

um:

x^{4} - 13 x^{2} + 36

x^{4} - 13 x^{2} + 36 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - 13 u + 36 = 0

Löse

u^{2} - 13 u + 36 = 0 : u = 9, u = 4

u = 9, u = 4

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} = 4 : x = 2, x = - 2

Die Lösungen sind

x = 3, x = - 3, x = 2, x = - 2

Graph

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