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Beliebt Algebra >

x^4-7x^2+1=0

Lösung

x^{4} - 7 x^{2} + 1 = 0

Lösung

x = \frac{7 + 3 5}{2}, x = - \frac{7 + 3 5}{2}, x = \frac{7 - 3 5}{2}, x = - \frac{7 - 3 5}{2}

+1

Dezimale

x = 2.61803 \dots, x = - 2.61803 \dots, x = 0.38196 \dots, x = - 0.38196 \dots

Schritte zur Lösung

x^{4} - 7 x^{2} + 1 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - 7 u + 1 = 0

Löse

u^{2} - 7 u + 1 = 0 : u = \frac{7 + 3 5}{2}, u = \frac{7 - 3 5}{2}

u = \frac{7 + 3 5}{2}, u = \frac{7 - 3 5}{2}

Setze

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

löse für

x

Löse

x^{2} = \frac{7 + 3 5}{2} : x = \frac{7 + 3 5}{2}, x = - \frac{7 + 3 5}{2}

Löse

x^{2} = \frac{7 - 3 5}{2} : x = \frac{7 - 3 5}{2}, x = - \frac{7 - 3 5}{2}

Die Lösungen sind

x = \frac{7 + 3 5}{2}, x = - \frac{7 + 3 5}{2}, x = \frac{7 - 3 5}{2}, x = - \frac{7 - 3 5}{2}

Graph

Beliebte Beispiele

11 x^{3} - 3 x + 1 = 3 x

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x^4-3x^3+x^2-3x=0

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3 x^{3} - 2 x^{2} - 7 x = 2