t^{-9}-9t^{-3}+8=0

Lösung

t^{- 9} - 9 t^{- 3} + 8 = 0

t = 1, t = - \frac{1}{2} + \frac{3}{2} i, t = - \frac{1}{2} - \frac{3}{2} i, t = \frac{3 1 + 33}{2 3 2}, t = \frac{3 1 + 33 ( - \frac{1}{2} + \frac{3}{2} i )}{2 3 2}, t = \frac{3 1 + 33 ( - \frac{1}{2} - \frac{3}{2} i )}{2 3 2}, t = 3 \frac{1 - 33}{16}, t = - 3 \frac{1 - 33}{16} \frac{1}{2} + 3 \frac{1 - 33}{16} \frac{3}{2} i, t = - 3 \frac{1 - 33}{16} \frac{1}{2} - 3 \frac{1 - 33}{16} \frac{3}{2} i

Schritte zur Lösung

t^{- 9} - 9 t^{- 3} + 8 = 0

Fasse zusammen

\frac{1}{t ^{9}} - \frac{9}{t ^{3}} + 8 = 0

Multipliziere mit dem kleinsten gemeinsamen Multiplikator

1 - 9 t^{6} + 8 t^{9} = 0

Löse

1 - 9 t^{6} + 8 t^{9} = 0 : t = 1, t = - \frac{1}{2} + \frac{3}{2} i, t = - \frac{1}{2} - \frac{3}{2} i, t = \frac{3 1 + 33}{2 3 2}, t = \frac{3 1 + 33 ( - \frac{1}{2} + \frac{3}{2} i )}{2 3 2}, t = \frac{3 1 + 33 ( - \frac{1}{2} - \frac{3}{2} i )}{2 3 2}, t = 3 \frac{1 - 33}{16}, t = - 3 \frac{1 - 33}{16} \frac{1}{2} + 3 \frac{1 - 33}{16} \frac{3}{2} i, t = - 3 \frac{1 - 33}{16} \frac{1}{2} - 3 \frac{1 - 33}{16} \frac{3}{2} i

t = 1, t = - \frac{1}{2} + \frac{3}{2} i, t = - \frac{1}{2} - \frac{3}{2} i, t = \frac{3 1 + 33}{2 3 2}, t = \frac{3 1 + 33 ( - \frac{1}{2} + \frac{3}{2} i )}{2 3 2}, t = \frac{3 1 + 33 ( - \frac{1}{2} - \frac{3}{2} i )}{2 3 2}, t = 3 \frac{1 - 33}{16}, t = - 3 \frac{1 - 33}{16} \frac{1}{2} + 3 \frac{1 - 33}{16} \frac{3}{2} i, t = - 3 \frac{1 - 33}{16} \frac{1}{2} - 3 \frac{1 - 33}{16} \frac{3}{2} i

Überprüfe die Lösungen

Bestimme unbestimmte (Singularitäts-)Punkte:

t = 0

Kombine die undefinierten Punkte mit den Lösungen:

t = 1, t = - \frac{1}{2} + \frac{3}{2} i, t = - \frac{1}{2} - \frac{3}{2} i, t = \frac{3 1 + 33}{2 3 2}, t = \frac{3 1 + 33 ( - \frac{1}{2} + \frac{3}{2} i )}{2 3 2}, t = \frac{3 1 + 33 ( - \frac{1}{2} - \frac{3}{2} i )}{2 3 2}, t = 3 \frac{1 - 33}{16}, t = - 3 \frac{1 - 33}{16} \frac{1}{2} + 3 \frac{1 - 33}{16} \frac{3}{2} i, t = - 3 \frac{1 - 33}{16} \frac{1}{2} - 3 \frac{1 - 33}{16} \frac{3}{2} i

6 - \frac{1}{x + 1} = \frac{6}{x + 2}

x + 2 + \frac{1}{x} = 0

\frac{1}{x} = \frac{3.55}{1.22}

so l v e f or p, \frac{1 - p}{p} = x

\frac{1}{t + 1} - 0.1 = 0