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Beliebt Algebra >

9z^4-3z^2+1=0

Lösung

9 z^{4} - 3 z^{2} + 1 = 0

Lösung

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

Schritte zur Lösung

9 z^{4} - 3 z^{2} + 1 = 0

Schreibe die Gleichung um mit

u = z^{2}

und

u^{2} = z^{4}

9 u^{2} - 3 u + 1 = 0

Löse

9 u^{2} - 3 u + 1 = 0 : u = \frac{1}{6} + i \frac{3}{6}, u = \frac{1}{6} - i \frac{3}{6}

u = \frac{1}{6} + i \frac{3}{6}, u = \frac{1}{6} - i \frac{3}{6}

Setze

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

löse für

z

Löse

z^{2} = \frac{1}{6} + i \frac{3}{6} : z = \frac{1}{2} + \frac{1}{2 3} i, z = - \frac{1}{2} - \frac{1}{2 3} i

Löse

z^{2} = \frac{1}{6} - i \frac{3}{6} : z = \frac{1}{2} - \frac{1}{2 3} i, z = - \frac{1}{2} + \frac{1}{2 3} i

Die Lösungen sind

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

Graph

Beliebte Beispiele

x^4+27x^2-324=0

x^{4} + 27 x^{2} - 324 = 0

x^4-2x^3+4x-1=0

x^{4} - 2 x^{3} + 4 x - 1 = 0

solvefor x,(x)8x^2+4y^2=12

so l v e f or x, (x) 8 x^{2} + 4 y^{2} = 12

x^{5} - 2 x = 0

solvefor x,x^4-10x^2+9=0

so l v e f or x, x^{4} - 10 x^{2} + 9 = 0