Question

Daca  x+$\frac{1}{x} =6$, atunci valoarea expresie $x^{2} + \frac{1}{ x^{2} }$ este egala cu .... ?

Answer 1

[tex]x+ \frac{1}{x}=6|^2 \Longrightarrow (x+ \frac{1}{x})^2=x^2+ \frac{1}{x^2}+2* x*\frac{1}{x} \\ \\ 6^2=x^2+ \frac{1}{x^2}+2 \\ \\ x^2+ \frac{1}{x^2}=36-2 \\ \\ \boxed{x^2+ \frac{1}{x^2}=34} [/tex]