6x^2-11x^4-2=0

Lösung

6 x^{2} - 11 x^{4} - 2 = 0

x = \frac{3 + 22}{22} - \frac{13}{22 \frac{3 + 22}{22}} i, x = - \frac{3 + 22}{22} + \frac{13}{22 \frac{3 + 22}{22}} i, x = \frac{3 + 22}{22} + \frac{13}{22 \frac{3 + 22}{22}} i, x = - \frac{3 + 22}{22} - \frac{13}{22 \frac{3 + 22}{22}} i

Schritte zur Lösung

6 x^{2} - 11 x^{4} - 2 = 0

Schreibe in der Standard Form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- 11 x^{4} + 6 x^{2} - 2 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

- 11 u^{2} + 6 u - 2 = 0

Löse

- 11 u^{2} + 6 u - 2 = 0 : u = \frac{3}{11} - i \frac{13}{11}, u = \frac{3}{11} + i \frac{13}{11}

u = \frac{3}{11} - i \frac{13}{11}, u = \frac{3}{11} + i \frac{13}{11}

Setze

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

löse für

x

Löse

x^{2} = \frac{3}{11} - i \frac{13}{11} : x = \frac{3 + 22}{22} - \frac{13}{22 \frac{3 + 22}{22}} i, x = - \frac{3 + 22}{22} + \frac{13}{22 \frac{3 + 22}{22}} i

Löse

x^{2} = \frac{3}{11} + i \frac{13}{11} : x = \frac{3 + 22}{22} + \frac{13}{22 \frac{3 + 22}{22}} i, x = - \frac{3 + 22}{22} - \frac{13}{22 \frac{3 + 22}{22}} i

Die Lösungen sind

x = \frac{3 + 22}{22} - \frac{13}{22 \frac{3 + 22}{22}} i, x = - \frac{3 + 22}{22} + \frac{13}{22 \frac{3 + 22}{22}} i, x = \frac{3 + 22}{22} + \frac{13}{22 \frac{3 + 22}{22}} i, x = - \frac{3 + 22}{22} - \frac{13}{22 \frac{3 + 22}{22}} i

10 x^{4} - 3 x^{2} + 1 = 0

x^{3} + 7 x^{2} - 4 x - 28 = 0

x^{4} - 2 x^{3} + x^{2} - 8 x - 12 = 0

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

12 x^{3} - 20 x^{2} + 11 x - 2 = 0