5x^4+15x^2+50=0

Lösung

5 x^{4} + 15 x^{2} + 50 = 0

x = \frac{- 3 + 2 10}{2} + \frac{31}{2 - 3 + 2 10} i, x = - \frac{- 3 + 2 10}{2} - \frac{31}{2 - 3 + 2 10} i, x = \frac{- 3 + 2 10}{2} - \frac{31}{2 - 3 + 2 10} i, x = - \frac{- 3 + 2 10}{2} + \frac{31}{2 - 3 + 2 10} i

Schritte zur Lösung

5 x^{4} + 15 x^{2} + 50 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

5 u^{2} + 15 u + 50 = 0

Löse

5 u^{2} + 15 u + 50 = 0 : u = - \frac{3}{2} + i \frac{31}{2}, u = - \frac{3}{2} - i \frac{31}{2}

u = - \frac{3}{2} + i \frac{31}{2}, u = - \frac{3}{2} - i \frac{31}{2}

Setze

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

löse für

x

Löse

x^{2} = - \frac{3}{2} + i \frac{31}{2} : x = \frac{- 3 + 2 10}{2} + \frac{31}{2 - 3 + 2 10} i, x = - \frac{- 3 + 2 10}{2} - \frac{31}{2 - 3 + 2 10} i

Löse

x^{2} = - \frac{3}{2} - i \frac{31}{2} : x = \frac{- 3 + 2 10}{2} - \frac{31}{2 - 3 + 2 10} i, x = - \frac{- 3 + 2 10}{2} + \frac{31}{2 - 3 + 2 10} i

Die Lösungen sind

x = \frac{- 3 + 2 10}{2} + \frac{31}{2 - 3 + 2 10} i, x = - \frac{- 3 + 2 10}{2} - \frac{31}{2 - 3 + 2 10} i, x = \frac{- 3 + 2 10}{2} - \frac{31}{2 - 3 + 2 10} i, x = - \frac{- 3 + 2 10}{2} + \frac{31}{2 - 3 + 2 10} i

3 x^{3} - 3 x^{2} - 7 x + 5 = x^{3} - 2 x^{2} - 1

0.75 = 10 x^{9} - 9 x^{10}

4 x^{3} - 9 x^{2} + 4 = 0

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

3 x^{3} + 4 x^{2} - 9 x - 12 = 0