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Beliebt Algebra >

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

Lösung

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

Lösung

x = - \frac{- 3 + 65}{4}, x = - - \frac{- 3 + 65}{4}, x = \frac{3 + 65}{2}, x = - \frac{3 + 65}{2}

Schritte zur Lösung

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

Schreibe in der Standard Form

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

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

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

- 2 u^{2} + 3 u + 7 = 0

Löse

- 2 u^{2} + 3 u + 7 = 0 : u = - \frac{- 3 + 65}{4}, u = \frac{3 + 65}{4}

u = - \frac{- 3 + 65}{4}, u = \frac{3 + 65}{4}

Setze

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

löse für

x

Löse

x^{2} = - \frac{- 3 + 65}{4} : x = - \frac{- 3 + 65}{4}, x = - - \frac{- 3 + 65}{4}

Löse

x^{2} = \frac{3 + 65}{4} : x = \frac{3 + 65}{2}, x = - \frac{3 + 65}{2}

Die Lösungen sind

x = - \frac{- 3 + 65}{4}, x = - - \frac{- 3 + 65}{4}, x = \frac{3 + 65}{2}, x = - \frac{3 + 65}{2}

Graph

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