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Beliebt Algebra >

2z^6-15z^3-27=0

Lösung

2 z^{6} - 15 z^{3} - 27 = 0

Lösung

z = 39, z = - 39 \frac{1}{2} + 39 \frac{3}{2} i, z = - 39 \frac{1}{2} - 39 \frac{3}{2} i, z = - 3 \frac{3}{2}, z = \frac{3 3}{2 3 2} - \frac{6 3 ^{5}}{2 3 2} i, z = \frac{3 3}{2 3 2} + \frac{6 3 ^{5}}{2 3 2} i

Schritte zur Lösung

2 z^{6} - 15 z^{3} - 27 = 0

Schreibe die Gleichung um mit

u = z^{3}

und

u^{2} = z^{6}

2 u^{2} - 15 u - 27 = 0

Löse

2 u^{2} - 15 u - 27 = 0 : u = 9, u = - \frac{3}{2}

u = 9, u = - \frac{3}{2}

Setze

u = z^{3} w i e d er e in,

löse für

z

Löse

z^{3} = 9 : z = 39, z = - 39 \frac{1}{2} + 39 \frac{3}{2} i, z = - 39 \frac{1}{2} - 39 \frac{3}{2} i

Löse

z^{3} = - \frac{3}{2} : z = - 3 \frac{3}{2}, z = \frac{3 3}{2 3 2} - \frac{6 3 ^{5}}{2 3 2} i, z = \frac{3 3}{2 3 2} + \frac{6 3 ^{5}}{2 3 2} i

Die Lösungen sind

z = 39, z = - 39 \frac{1}{2} + 39 \frac{3}{2} i, z = - 39 \frac{1}{2} - 39 \frac{3}{2} i, z = - 3 \frac{3}{2}, z = \frac{3 3}{2 3 2} - \frac{6 3 ^{5}}{2 3 2} i, z = \frac{3 3}{2 3 2} + \frac{6 3 ^{5}}{2 3 2} i

Graph

Beliebte Beispiele

(x^2+7x+49)(x-7)=218

(x^{2} + 7 x + 49) (x - 7) = 218

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w+w^2-w^3+w^4=5

w + w^{2} - w^{3} + w^{4} = 5