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Beliebt Algebra >

2x^6-17x^3+8=0

Lösung

2 x^{6} - 17 x^{3} + 8 = 0

Lösung

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

Schritte zur Lösung

2 x^{6} - 17 x^{3} + 8 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

2 u^{2} - 17 u + 8 = 0

Löse

2 u^{2} - 17 u + 8 = 0 : u = 8, u = \frac{1}{2}

u = 8, u = \frac{1}{2}

Setze

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

löse für

x

Löse

x^{3} = 8 : x = 2, x = - 1 + 3 i, x = - 1 - 3 i

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

8a^3-12a^2+6a+215=0

8 a^{3} - 12 a^{2} + 6 a + 215 = 0

9x^4-3x^3+34x^2-12x-8=0

9 x^{4} - 3 x^{3} + 34 x^{2} - 12 x - 8 = 0

a^{3} - 44 a + 48 = 0

x^{3} + x = 0

x + x^{3} = 0