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Beliebt Algebra >

(x^2-2)^2-10(x^2-2)+21=0

Lösung

(x^{2} - 2)^{2} - 10 (x^{2} - 2) + 21 = 0

Lösung

x = 3, x = - 3, x = 5, x = - 5

+1

Dezimale

x = 3, x = - 3, x = 2.23606 \dots, x = - 2.23606 \dots

Schritte zur Lösung

(x^{2} - 2)^{2} - 10 (x^{2} - 2) + 21 = 0

Schreibe

(x^{2} - 2)^{2} - 10 (x^{2} - 2) + 21

um:

x^{4} - 14 x^{2} + 45

x^{4} - 14 x^{2} + 45 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - 14 u + 45 = 0

Löse

u^{2} - 14 u + 45 = 0 : u = 9, u = 5

u = 9, u = 5

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} = 5 : x = 5, x = - 5

Die Lösungen sind

x = 3, x = - 3, x = 5, x = - 5

Graph

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