[tex]1+3+3^2+\dots +3^{101}[/tex] este suma unei progresii geometrice cu ratia 3. Deci, [tex]1+3+3^2+\dots +3^{101} =1 \cdot \dfrac{3^{102}-1}{3-1}= \dfrac{3^{102}-1}{2}[/tex] .
[tex] x^2-1 = 2 \cdot \dfrac{3^{102}-1}{2} \iff x^2-1 = 3^{102}-1[/tex] adica [tex]x^2=3^{102} \implies x = 3^{51}[/tex]
