((x^{-2}))/x = 1/((x^{12))}

Lösung

\frac{( x ^{- 2} )}{x} = \frac{1}{( x ^{12} )}

x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = cos (\frac{2 π}{9}) + i sin (\frac{2 π}{9}), x = cos (\frac{8 π}{9}) + i sin (\frac{8 π}{9}), x = cos (\frac{14 π}{9}) + i sin (\frac{14 π}{9}), x = cos (\frac{2 π}{9}) - i sin (\frac{2 π}{9}), x = cos (\frac{4 π}{9}) + i sin (\frac{4 π}{9}), x = cos (\frac{10 π}{9}) + i sin (\frac{10 π}{9})

Schritte zur Lösung

\frac{( x ^{- 2} )}{x} = \frac{1}{( x ^{12} )}

Fasse zusammen

\frac{1}{x ^{3}} = \frac{1}{x ^{12}}

Kreuzmultiplizieren

x^{12} = x^{3}

Löse

x^{12} = x^{3} : x = 0, x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = cos (\frac{2 π}{9}) + i sin (\frac{2 π}{9}), x = cos (\frac{8 π}{9}) + i sin (\frac{8 π}{9}), x = cos (\frac{14 π}{9}) + i sin (\frac{14 π}{9}), x = cos (\frac{2 π}{9}) - i sin (\frac{2 π}{9}), x = cos (\frac{4 π}{9}) + i sin (\frac{4 π}{9}), x = cos (\frac{10 π}{9}) + i sin (\frac{10 π}{9})

x = 0, x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = cos (\frac{2 π}{9}) + i sin (\frac{2 π}{9}), x = cos (\frac{8 π}{9}) + i sin (\frac{8 π}{9}), x = cos (\frac{14 π}{9}) + i sin (\frac{14 π}{9}), x = cos (\frac{2 π}{9}) - i sin (\frac{2 π}{9}), x = cos (\frac{4 π}{9}) + i sin (\frac{4 π}{9}), x = cos (\frac{10 π}{9}) + i sin (\frac{10 π}{9})

Überprüfe die Lösungen

Bestimme unbestimmte (Singularitäts-)Punkte:

x = 0

Da die Gleichung undefiniert ist für:

0

x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = cos (\frac{2 π}{9}) + i sin (\frac{2 π}{9}), x = cos (\frac{8 π}{9}) + i sin (\frac{8 π}{9}), x = cos (\frac{14 π}{9}) + i sin (\frac{14 π}{9}), x = cos (\frac{2 π}{9}) - i sin (\frac{2 π}{9}), x = cos (\frac{4 π}{9}) + i sin (\frac{4 π}{9}), x = cos (\frac{10 π}{9}) + i sin (\frac{10 π}{9})

\frac{( x - 6 )}{( x + 4 )} = 0

2 x^{- 5} = (16)^{2}

(\frac{x + 1}{x})^{2} = \frac{4 + 3}{2 ( x - \frac{1}{x} )}

5 \frac{x}{x - 5} + ∣ x ∣ = \frac{x ^{2}}{∣ x - 5 ∣}

\frac{3}{4 \cdot m + 2 m} = 22