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Beliebt Algebra >

(x^2-7)^2+4(x^2-7)-5=0

Lösung

(x^{2} - 7)^{2} + 4 (x^{2} - 7) - 5 = 0

Lösung

x = 22, x = - 22, x = 2, x = - 2

+1

Dezimale

x = 2.82842 \dots, x = - 2.82842 \dots, x = 1.41421 \dots, x = - 1.41421 \dots

Schritte zur Lösung

(x^{2} - 7)^{2} + 4 (x^{2} - 7) - 5 = 0

Schreibe

(x^{2} - 7)^{2} + 4 (x^{2} - 7) - 5

um:

x^{4} - 10 x^{2} + 16

x^{4} - 10 x^{2} + 16 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - 10 u + 16 = 0

Löse

u^{2} - 10 u + 16 = 0 : u = 8, u = 2

u = 8, u = 2

Setze

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

löse für

x

Löse

x^{2} = 8 : x = 22, x = - 22

Löse

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

Die Lösungen sind

x = 22, x = - 22, x = 2, x = - 2

Graph

Beliebte Beispiele

- 2 x^{4} + 5 = 13

x^{12} - 1 = 4

7 π k^{3} = 22704

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

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

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