x^4+1/(x^4)=47

Lösung

x^{4} + \frac{1}{x ^{4}} = 47

x = 4 \frac{47 + 21 5}{2}, x = - 4 \frac{47 + 21 5}{2}, x = i 4 \frac{47 + 21 5}{2}, x = - i 4 \frac{47 + 21 5}{2}, x = 4 \frac{47 - 21 5}{2}, x = - 4 \frac{47 - 21 5}{2}, x = i 4 \frac{47 - 21 5}{2}, x = - i 4 \frac{47 - 21 5}{2}

Schritte zur Lösung

x^{4} + \frac{1}{x ^{4}} = 47

Multipliziere beide Seiten mit

x^{4}

x^{8} + 1 = 47 x^{4}

Löse

x^{8} + 1 = 47 x^{4} : x = 4 \frac{47 + 21 5}{2}, x = - 4 \frac{47 + 21 5}{2}, x = i 4 \frac{47 + 21 5}{2}, x = - i 4 \frac{47 + 21 5}{2}, x = 4 \frac{47 - 21 5}{2}, x = - 4 \frac{47 - 21 5}{2}, x = i 4 \frac{47 - 21 5}{2}, x = - i 4 \frac{47 - 21 5}{2}

x = 4 \frac{47 + 21 5}{2}, x = - 4 \frac{47 + 21 5}{2}, x = i 4 \frac{47 + 21 5}{2}, x = - i 4 \frac{47 + 21 5}{2}, x = 4 \frac{47 - 21 5}{2}, x = - 4 \frac{47 - 21 5}{2}, x = i 4 \frac{47 - 21 5}{2}, x = - i 4 \frac{47 - 21 5}{2}

Überprüfe die Lösungen

Bestimme unbestimmte (Singularitäts-)Punkte:

x = 0

Kombine die undefinierten Punkte mit den Lösungen:

x = 4 \frac{47 + 21 5}{2}, x = - 4 \frac{47 + 21 5}{2}, x = i 4 \frac{47 + 21 5}{2}, x = - i 4 \frac{47 + 21 5}{2}, x = 4 \frac{47 - 21 5}{2}, x = - 4 \frac{47 - 21 5}{2}, x = i 4 \frac{47 - 21 5}{2}, x = - i 4 \frac{47 - 21 5}{2}

\frac{2 x - 4}{x - 2} = \frac{1}{3}

x^{- 2} - 5 x^{- 1} - 6 = 0

\frac{4}{x} - \frac{9}{x + 1} = 2

41 y^{- 4} - 58 y^{- 2} + 1 = 0

- \frac{x}{2 x - 3} = \frac{2}{5 x + 3}