3x^4+15x^2-17=0

Lösung

3 x^{4} + 15 x^{2} - 17 = 0

x = \frac{- 15 + 429}{6}, x = - \frac{- 15 + 429}{6}, x = \frac{- 15 - 429}{6}, x = - \frac{- 15 - 429}{6}

Schritte zur Lösung

3 x^{4} + 15 x^{2} - 17 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

3 u^{2} + 15 u - 17 = 0

Löse

3 u^{2} + 15 u - 17 = 0 : u = \frac{- 15 + 429}{6}, u = \frac{- 15 - 429}{6}

u = \frac{- 15 + 429}{6}, u = \frac{- 15 - 429}{6}

Setze

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

löse für

x

Löse

x^{2} = \frac{- 15 + 429}{6} : x = \frac{- 15 + 429}{6}, x = - \frac{- 15 + 429}{6}

Löse

x^{2} = \frac{- 15 - 429}{6} : x = \frac{- 15 - 429}{6}, x = - \frac{- 15 - 429}{6}

Die Lösungen sind

x = \frac{- 15 + 429}{6}, x = - \frac{- 15 + 429}{6}, x = \frac{- 15 - 429}{6}, x = - \frac{- 15 - 429}{6}

- x^{3} + 4 x^{2} - 6 x + 4 = 0

12 y^{3} + 24 y^{2} = 3 y + 6

x (x + 10) (x^{2} - 5) = 0

x^{3} + 3 x^{2} - 14 x - 42 = 0

a^{9} = 17 + (9 - 1) - 8