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Beliebt Algebra >

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

Lösung

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

Lösung

x = 2 (2 + 3), x = - 2 (2 + 3), x = 2 (2 - 3), x = - 2 (2 - 3)

+1

Dezimale

x = 2.73205 \dots, x = - 2.73205 \dots, x = 0.73205 \dots, x = - 0.73205 \dots

Schritte zur Lösung

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

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - 8 u + 4 = 0

Löse

u^{2} - 8 u + 4 = 0 : u = 2 (2 + 3), u = 2 (2 - 3)

u = 2 (2 + 3), u = 2 (2 - 3)

Setze

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

löse für

x

Löse

x^{2} = 2 (2 + 3) : x = 2 (2 + 3), x = - 2 (2 + 3)

Löse

x^{2} = 2 (2 - 3) : x = 2 (2 - 3), x = - 2 (2 - 3)

Die Lösungen sind

x = 2 (2 + 3), x = - 2 (2 + 3), x = 2 (2 - 3), x = - 2 (2 - 3)

Graph

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