Question

найдите все двухзначные числа если ab+ba=121

Answer 1

$a neq 0, b neq 0\ a, b in {1, 2, 3, 4, 5, 6, 7, 8, 9}, \ bar{ab}+bar{ba}=121, \ bar{ab}+bar{ba}=10a+b+10b+a=11a+11b=11(a+b), \ 11(a+b)=121, \ a+b=11, \ b=11-a, \ a neq 1, b neq 1, \ a=2, b=9, \ a=3, b=8, \ a=4, b=7, \ a=5, b=6, \ a=6, b=5, \ a=7, b=4, \ a=8, b=3, \ a=9, b=2, \ 29, 38, 47, 56, 65, 74, 83, 92.$