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Beliebt Algebra >

20x^4+160x^2-285=0

Lösung

20 x^{4} + 160 x^{2} - 285 = 0

Lösung

x = \frac{3}{2}, x = - \frac{3}{2}, x = \frac{19}{2} i, x = - \frac{19}{2} i

Schritte zur Lösung

20 x^{4} + 160 x^{2} - 285 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

20 u^{2} + 160 u - 285 = 0

Löse

20 u^{2} + 160 u - 285 = 0 : u = \frac{3}{2}, u = - \frac{19}{2}

u = \frac{3}{2}, u = - \frac{19}{2}

Setze

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

löse für

x

Löse

x^{2} = \frac{3}{2} : x = \frac{3}{2}, x = - \frac{3}{2}

Löse

x^{2} = - \frac{19}{2} : x = \frac{19}{2} i, x = - \frac{19}{2} i

Die Lösungen sind

x = \frac{3}{2}, x = - \frac{3}{2}, x = \frac{19}{2} i, x = - \frac{19}{2} i

Graph

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59 = \frac{1}{4} (75 x - x^{3})

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