Question

toate solutile pentru aba+bab=777

Answer 1

$\overline{aba}+\overline{bab}=777\\ \\ 100a+10b+a+100b+10a+b=777\\ \\ 111a+111b=777\\ \\ 111(a+b)=777 \ |:111\\ \\ a+b=7\\ \\ a=1 \Rightarrow b=7-1=6\\ \\ a=2 \Rightarrow b=7-2=5\\ \\ a=3 \Rightarrow b=7-3=4\\ \\ a=4 \Rightarrow b=7-4=3\\ \\ a=5 \Rightarrow b=7-5=2\\ \\ a=6 \Rightarrow b=7-6=1\\ \\ S=\{ (1, \ 6); \ (2, \ 5); \ (3, \ 4); \ (4, \ 3); \ (5, \ 2); \ (6, \ 1)\}$