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Beliebt Algebra >

x^4-5x^2-8=0

Lösung

x^{4} - 5 x^{2} - 8 = 0

Lösung

x = \frac{5 + 57}{2}, x = - \frac{5 + 57}{2}, x = \frac{5 - 57}{2}, x = - \frac{5 - 57}{2}

Schritte zur Lösung

x^{4} - 5 x^{2} - 8 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - 5 u - 8 = 0

Löse

u^{2} - 5 u - 8 = 0 : u = \frac{5 + 57}{2}, u = \frac{5 - 57}{2}

u = \frac{5 + 57}{2}, u = \frac{5 - 57}{2}

Setze

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

löse für

x

Löse

x^{2} = \frac{5 + 57}{2} : x = \frac{5 + 57}{2}, x = - \frac{5 + 57}{2}

Löse

x^{2} = \frac{5 - 57}{2} : x = \frac{5 - 57}{2}, x = - \frac{5 - 57}{2}

Die Lösungen sind

x = \frac{5 + 57}{2}, x = - \frac{5 + 57}{2}, x = \frac{5 - 57}{2}, x = - \frac{5 - 57}{2}

Graph

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