[tex]\overline{2a}+\overline{3b}=p^2\\ \\ 20\leq \overline{2a}\leq 29\\ \\ 30\leq \overline{3b}\leq 39\\ \\ 50 \leq \overline{2a}+\overline{3b} \leq 68\\ \\ 50\leq p^2 \leq 68 \\ \\ \Rightarrow p^2=64 \Rightarrow \overline{2a}+\overline{3b}=64\\ \\ 20+a+30+b=64 \\ \\ \Rightarrow 50+a+b=64 \Rightarrow a+b=14\\ \\ a, \ b\in \{0, \ 1, \ 2, \ 3, \ 4, \ ... \ 9 \} \\ \\ Cazul \ 1: \\ \\ a=9 \Rightarrow b=14-9=5\\ \\ Cazul \ 2: \\ \\ a=8 \Rightarrow b=14-8=6\\ \\Cazul \ 3: \\ \\ a=7 \Rightarrow b=14-7=7\\ \\ Cazul \ 4: \\ \\ a=6 \Rightarrow b=14-6=8\\ \\ Cazul \ 1: \\ \\ a=5 \Rightarrow b=14-5=9\\ \\ S=\{(9, \ 5); \ (8, \ 6); \ (7, \ 7); \ (6, \ 8); \ (5, \ 9) \}[/tex]
