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Beliebt Algebra >

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

Lösung

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

Lösung

x = \frac{1}{2} + \frac{7}{2} i, x = - \frac{1}{2} - \frac{7}{2} i, x = \frac{1}{2} - \frac{7}{2} i, x = - \frac{1}{2} + \frac{7}{2} i

Schritte zur Lösung

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

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} + 3 u + 4 = 0

Löse

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

u = - \frac{3}{2} + i \frac{7}{2}, u = - \frac{3}{2} - i \frac{7}{2}

Setze

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

löse für

x

Löse

x^{2} = - \frac{3}{2} + i \frac{7}{2} : x = \frac{1}{2} + \frac{7}{2} i, x = - \frac{1}{2} - \frac{7}{2} i

Löse

x^{2} = - \frac{3}{2} - i \frac{7}{2} : x = \frac{1}{2} - \frac{7}{2} i, x = - \frac{1}{2} + \frac{7}{2} i

Die Lösungen sind

x = \frac{1}{2} + \frac{7}{2} i, x = - \frac{1}{2} - \frac{7}{2} i, x = \frac{1}{2} - \frac{7}{2} i, x = - \frac{1}{2} + \frac{7}{2} i

Graph

Beliebte Beispiele

solvefor y,y^7=5x^4+9x

so l v e f or y, y^{7} = 5 x^{4} + 9 x

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

2 = 2 x^{6} x^{796}

2x^3+3x^2-5x-6=0

2 x^{3} + 3 x^{2} - 5 x - 6 = 0

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

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