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Beliebt Algebra >

x^4+2x^2+4=0

Lösung

x^{4} + 2 x^{2} + 4 = 0

Lösung

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

Schritte zur Lösung

x^{4} + 2 x^{2} + 4 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} + 2 u + 4 = 0

Löse

u^{2} + 2 u + 4 = 0 : u = - 1 + 3 i, u = - 1 - 3 i

u = - 1 + 3 i, u = - 1 - 3 i

Setze

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

löse für

x

Löse

x^{2} = - 1 + 3 i : x = \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i

Löse

x^{2} = - 1 - 3 i : x = \frac{1}{2} - \frac{3}{2} i, x = - \frac{1}{2} + \frac{3}{2} i

Die Lösungen sind

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

Graph

Beliebte Beispiele

5y^3+17y-12=9y^2-9y

5 y^{3} + 17 y - 12 = 9 y^{2} - 9 y

4x+3=x^3+3x^2-9x-12

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

x^{3} - x^{2} - 5 x - 3 = 0

5x^3+23x^2+20x-12=0

5 x^{3} + 23 x^{2} + 20 x - 12 = 0

x^{3} - x - 3360 = 0