[tex] x-\frac{1}{x} =4 => \frac{x^{2}-1 }{x} =4[/tex]
[tex] x^{2} + \frac{1}{ x^{2} } = \frac{ x^{4}+1 }{ x^{2} } [/tex]
Ridicam la puterea a 2-a prima fractie si vom avea:
[tex] \frac{ ( x^{2}-1) ^{2} }{ x^{2} } =16 => \frac{ x^{4}+1-2 x^{2} }{ x^{2} } =16 => \frac{ x^{4}+1 }{ x^{2} } - \frac{2 x^{2} }{ x^{2} } =16 => \frac{ x^{4}+1 }{ x^{2} } =18[/tex]
Deci: [tex] x^{2} + \frac{1}{ x^{2} } =18[/tex]
