5x^4+7x^2-12=0

Lösung

5 x^{4} + 7 x^{2} - 12 = 0

x = 1, x = - 1, x = \frac{2 3}{5} i, x = - \frac{2 3}{5} i

Schritte zur Lösung

5 x^{4} + 7 x^{2} - 12 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

5 u^{2} + 7 u - 12 = 0

Löse

5 u^{2} + 7 u - 12 = 0 : u = 1, u = - \frac{12}{5}

u = 1, u = - \frac{12}{5}

Setze

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

löse für

x

Löse

x^{2} = 1 : x = 1, x = - 1

Löse

x^{2} = - \frac{12}{5} : x = \frac{2 3}{5} i, x = - \frac{2 3}{5} i

Die Lösungen sind

x = 1, x = - 1, x = \frac{2 3}{5} i, x = - \frac{2 3}{5} i

roo t s x^{3} + 4 x^{2} + x - 6

x^{4} - 3 x^{3} - 13 x^{2} + 9 x + 30 = 0

7 y^{5} - 3 y^{1} = 2 y^{2}

3 x^{3} + 2 x^{2} - 19 x + 6 = 0

r a t i o na l roo t s t es t x^{3} - 3 x^{2} - 25 x + 75 = 0