[tex]x+\frac{1}{x} = 2\,\big|^2[/tex] (Ridic la pătrat)
[tex]\Rightarrow \left(x+\frac{1}{x}\right)^2 = 2^2[/tex]
[tex]\Rightarrow x^2+2\cdot x\cdot \frac{1}{x}+\left(\frac{1}{x}\right)^2 = 4[/tex]
[tex]\Rightarrow x^2+2\cdot 1+\frac{1}{x^2} = 4[/tex]
[tex]\Rightarrow x^2+2+\frac{1}{x^2} = 4[/tex]
[tex]\Rightarrow x^2+\frac{1}{x^2} = 4-2[/tex]
[tex]\Rightarrow x^2+\frac{1}{x^2} = 2\,\,\,\,\checkmark[/tex]
