Răspuns:
ab ∈ {19, 28, 37, 46, 64, 73, 82, 91}
Explicație pas cu pas:
a, b cifre
a≠b
a ≠ 0; b ≠ 0
a,b ∈ {1,2,3....,9}
ab + ba = 110 descompunem in baza 10
10a + b + 10b + a = 110
11a + 11b = 110 / : 11
a + b = 10 => a = 10 - b
a = 1 => b = 9 ab = 19 (solutie)
a = 2 => b = 8 ab = 28 (solutie)
a = 3 => b = 7 ab = 37 (solutie)
a = 4 => b = 6 ab = 46 (solutie)
a = 5 => b = 5 NU CONVINE deoarece a ≠ b
a = 6 => b = 4 ab = 64 (solutie)
a = 7 => b = 3 ab = 73 (solutie)
a = 8 => b = 2 ab = 82 (solutie)
a = 9 => b = 1 ab = 91 (solutie)
ab ∈ {19, 28, 37, 46, 64, 73, 82, 91}
