(x+1/x)^2=3

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

(x + \frac{1}{x})^{2} : x^{2} + 2 + \frac{1}{x ^{2}}

x^{2} + 2 + \frac{1}{x ^{2}} = 3

Multipliziere beide Seiten mit

x^{2}

x^{4} + 2 x^{2} + 1 = 3 x^{2}

Löse

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

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

\frac{1}{5 m} = \frac{- 2}{3}

\frac{4}{x} + x = 5

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

a^{- n} = \frac{1}{a ^{n}}

\frac{5}{2 x} + 3 = \frac{6}{x} - 2