[tex](x-\sqrt{13})(x+\sqrt{13})=4y^2\\
x^2-13=4y^2\\
x^2-4y^2=13\\
(x-2y)(x+2y)=13\\
\text{De aici deducem doua variante posibile:}\\
i) \left \{ {{x-2y=1} \atop {x+2y=13}} \right.,\text{de unde }x=7\text{ si }y=3\\
ii) \left \{ {{x-2y=13} \atop {x+2y=1}} \right. ,\text{de unde x=7 si y=-3}(\text{solutie care nu convine})\\
\text{Deci raspunsul este a)}\\
\text{Obs:Am folosit identitatea }\boxed{(a-b)(a+b)=a^2-b^2} [/tex]
