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Beliebt Algebra >

-w^4+60w^2-96=0

Lösung

- w^{4} + 60 w^{2} - 96 = 0

Lösung

w = 2 (15 - 201), w = - 2 (15 - 201), w = 2 (15 + 201), w = - 2 (15 + 201)

+1

Dezimale

w = 1.28261 \dots, w = - 1.28261 \dots, w = 7.63903 \dots, w = - 7.63903 \dots

Schritte zur Lösung

- w^{4} + 60 w^{2} - 96 = 0

Schreibe die Gleichung um mit

u = w^{2}

und

u^{2} = w^{4}

- u^{2} + 60 u - 96 = 0

Löse

- u^{2} + 60 u - 96 = 0 : u = 2 (15 - 201), u = 2 (15 + 201)

u = 2 (15 - 201), u = 2 (15 + 201)

Setze

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

löse für

w

Löse

w^{2} = 2 (15 - 201) : w = 2 (15 - 201), w = - 2 (15 - 201)

Löse

w^{2} = 2 (15 + 201) : w = 2 (15 + 201), w = - 2 (15 + 201)

Die Lösungen sind

w = 2 (15 - 201), w = - 2 (15 - 201), w = 2 (15 + 201), w = - 2 (15 + 201)

Graph

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