[tex]\text{Notam cu:} S_k=x_1^k+x_2^k\\
\text{Avem ca:} S_{k+2}=-S_{k+1}+S_k,\text{iar}\ S_0=2,S_1=-1\\
\text{Ecuatia caracteristica este:}\\
r^2+r-1=0\\
\Delta=5\\
r_1=\dfrac{-1+\sqrt{5}}{2},r_2=\dfrac{-1-\sqrt{5}}{2}\\
S_k=\left(\dfrac{-1+\sqrt{5}}{2}\right)^k\cdot a+\left(\dfrac{-1-\sqrt5}{2}\right)^k\cdot b\\
\text{Ii afli pe a si pe b,si apoi ii simplu}.\\
\text{Sau poti sa afli radacinile ecuatiei si pur si simplu sa calculezi.}[/tex]
