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Beliebt Algebra >

x^4-265x^2+1=0

Lösung

x^{4} - 265 x^{2} + 1 = 0

Lösung

x = \frac{265 + 70221}{2}, x = - \frac{265 + 70221}{2}, x = \frac{265 - 70221}{2}, x = - \frac{265 - 70221}{2}

+1

Dezimale

x = 16.27870 \dots, x = - 16.27870 \dots, x = 0.06142 \dots, x = - 0.06142 \dots

Schritte zur Lösung

x^{4} - 265 x^{2} + 1 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - 265 u + 1 = 0

Löse

u^{2} - 265 u + 1 = 0 : u = \frac{265 + 70221}{2}, u = \frac{265 - 70221}{2}

u = \frac{265 + 70221}{2}, u = \frac{265 - 70221}{2}

Setze

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

löse für

x

Löse

x^{2} = \frac{265 + 70221}{2} : x = \frac{265 + 70221}{2}, x = - \frac{265 + 70221}{2}

Löse

x^{2} = \frac{265 - 70221}{2} : x = \frac{265 - 70221}{2}, x = - \frac{265 - 70221}{2}

Die Lösungen sind

x = \frac{265 + 70221}{2}, x = - \frac{265 + 70221}{2}, x = \frac{265 - 70221}{2}, x = - \frac{265 - 70221}{2}

Graph

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