Răspuns:
Explicație pas cu pas:
10a + b - 10b - a = 27
9a - 9b = 27
9(a - b) = 27
a - b = 27 : 9 = 3
a si b pot lua valori intre 1 si 9.
b = 1; a = 4; 14 + 41 + 2 = 57
b = 2; a = 5; 25 + 52 + 2 = 79
b = 3; a = 6; 36 + 63 + 2 = 101
b = 4; a = 7; 47 + 74 + 2 = 123
b = 5; a = 8; 58 + 85 + 2 = 145
b = 6; a = 9; 69 + 96 + 2 = 167
[tex]\it \overline{ab}-\overline{ba}=27\Rightarrow 10a+b-10b-a=27 \Rightarrow 9a-9b=27 \Rightarrow9(a-b) =27|_{:9}\Rightarrow\\ \\ \\ \Rightarrow a-b=3 \Rightarrow \overline{ab}\in\{41,\ 52,\ 63,\ 74,\ 85,\ 96\} \Rightarrow \overline{ba}\in\{14,25,36,47,58,69\}\\ \\ \\ \overline{ab}+\overline{ab}+2\in\{57,\ 79,\ 101,\ 123,\ 145,\ 167\}[/tex]
