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Beliebt Algebra >

x^4-x^2-c=0

Lösung

x^{4} - x^{2} - c = 0

Lösung

x = \frac{1 + 1 + 4 c}{2}, x = - \frac{1 + 1 + 4 c}{2}, x = \frac{1 - 1 + 4 c}{2}, x = - \frac{1 - 1 + 4 c}{2}

Schritte zur Lösung

x^{4} - x^{2} - c = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - u - c = 0

Löse

u^{2} - u - c = 0 : u = \frac{1 + 1 + 4 c}{2}, u = \frac{1 - 1 + 4 c}{2}

u = \frac{1 + 1 + 4 c}{2}, u = \frac{1 - 1 + 4 c}{2}

Setze

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

löse für

x

Löse

x^{2} = \frac{1 + 1 + 4 c}{2} : x = \frac{1 + 1 + 4 c}{2}, x = - \frac{1 + 1 + 4 c}{2}

Löse

x^{2} = \frac{1 - 1 + 4 c}{2} : x = \frac{1 - 1 + 4 c}{2}, x = - \frac{1 - 1 + 4 c}{2}

Die Lösungen sind

x = \frac{1 + 1 + 4 c}{2}, x = - \frac{1 + 1 + 4 c}{2}, x = \frac{1 - 1 + 4 c}{2}, x = - \frac{1 - 1 + 4 c}{2}

Graph

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