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Beliebt Algebra >

20x^4-x^2-1=0

Lösung

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

Lösung

x = \frac{1}{2}, x = - \frac{1}{2}, x = \frac{1}{5} i, x = - \frac{1}{5} i

Schritte zur Lösung

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

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

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

Löse

20 u^{2} - u - 1 = 0 : u = \frac{1}{4}, u = - \frac{1}{5}

u = \frac{1}{4}, u = - \frac{1}{5}

Setze

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

löse für

x

Löse

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

Löse

x^{2} = - \frac{1}{5} : x = \frac{1}{5} i, x = - \frac{1}{5} i

Die Lösungen sind

x = \frac{1}{2}, x = - \frac{1}{2}, x = \frac{1}{5} i, x = - \frac{1}{5} i

Graph

Beliebte Beispiele

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