de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

x^8+2x^6-x^4-2x^2+1=0

Lösung

x^{8} + 2 x^{6} - x^{4} - 2 x^{2} + 1 = 0

Lösung

x = \frac{9.6568 E 13}{1.5625 E 14}, x = - \frac{9.6568 E 13}{1.5625 E 14}, x = \frac{6.18033 E 15}{1.0 E 16}, x = - \frac{6.18033 E 15}{1.0 E 16}

+1

Dezimale

x = 0.78615 \dots, x = - 0.78615 \dots, x = 0.78615 \dots, x = - 0.78615 \dots

Schritte zur Lösung

x^{8} + 2 x^{6} - x^{4} - 2 x^{2} + 1 = 0

Schreibe die Gleichung um mit

u = x^{2}, u^{2} = x^{4}, u^{3} = x^{6}

und

u^{4} = x^{8}

u^{4} + 2 u^{3} - u^{2} - 2 u + 1 = 0

Löse

u^{4} + 2 u^{3} - u^{2} - 2 u + 1 = 0 : u \approx 0.61803 \dots, u \approx 0.61803 \dots, u \approx - 1.61803 \dots, u = - \frac{1597}{987}

u \approx 0.61803 \dots, u \approx 0.61803 \dots, u \approx - 1.61803 \dots, u = - \frac{1597}{987}

Setze

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

löse für

x

Löse

x^{2} = 0.61803 \dots : x = \frac{9.6568 E 13}{1.5625 E 14}, x = - \frac{9.6568 E 13}{1.5625 E 14}

Löse

x^{2} = 0.61803 \dots : x = \frac{6.18033 E 15}{1.0 E 16}, x = - \frac{6.18033 E 15}{1.0 E 16}

Löse

x^{2} = - 1.61803 \dots :

Keine Lösung für

x \in R

Löse

x^{2} = - \frac{1597}{987} :

Keine Lösung für

x \in R

Die Lösungen sind

x = \frac{9.6568 E 13}{1.5625 E 14}, x = - \frac{9.6568 E 13}{1.5625 E 14}, x = \frac{6.18033 E 15}{1.0 E 16}, x = - \frac{6.18033 E 15}{1.0 E 16}

Graph

Beliebte Beispiele

2x(x-8)(3x-2)=0

2 x (x - 8) (3 x - 2) = 0

x^4+5x^3+5x^2+5x+2=0

x^{4} + 5 x^{3} + 5 x^{2} + 5 x + 2 = 0

(x-1)^3+(x-1)^2=0

(x - 1)^{3} + (x - 1)^{2} = 0

x^{3} = \frac{50}{π}

(x^2+2)^2=2(x^2+6)

(x^{2} + 2)^{2} = 2 (x^{2} + 6)