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Beliebt Algebra >

8x^6-9x^3+1=0

Lösung

8 x^{6} - 9 x^{3} + 1 = 0

Lösung

x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i

Schritte zur Lösung

8 x^{6} - 9 x^{3} + 1 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

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

Löse

8 u^{2} - 9 u + 1 = 0 : u = 1, u = \frac{1}{8}

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

Setze

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

löse für

x

Löse

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

Löse

x^{3} = \frac{1}{8} : x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i

Die Lösungen sind

x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i

Graph

Beliebte Beispiele

4 x^{4} = 16 x^{2} - 16

x^{8} + 24 x^{4} = 25

(1 + x)^{9} = 2

a^{3} = 3

solvefor y,x+y^3=27

so l v e f or y, x + y^{3} = 27