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Beliebt Algebra >

4x^4-4x^2-1=0

Lösung

4 x^{4} - 4 x^{2} - 1 = 0

Lösung

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

Schritte zur Lösung

4 x^{4} - 4 x^{2} - 1 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

4 u^{2} - 4 u - 1 = 0

Löse

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

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

Setze

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

löse für

x

Löse

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

Löse

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

Die Lösungen sind

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

Graph

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