[tex]\displaystyle\bf\\x+\frac{1}{x}=6~~\Big|~Ridicam~puterea~a~2-a.\\\\\Bigg(x+\frac{1}{x}\Bigg)^2=6^2\\\\x^2+2\cdot x\cdot\frac{1}{x}+\Bigg(\frac{1}{x}\Bigg)^2=6^2\\\\x^2+\frac{2x}{x}+\frac{1}{x^2}=36\\\\x^2+2+\frac{1}{x^2}=36\\\\x^2+\frac{1}{x^2}=36-2\\\\\boxed{\bf x^2+\frac{1}{x^2}=34}[/tex]
