Răspuns: [tex]\red{\bf~ \overline{ab}~\in~\big\{ 61, 72, 83, 94\big\}}[/tex]
Explicație pas cu pas:
[tex]\bf \overline{ab}[/tex]
a > b
a si b sunt cifre
Cifrele sunt: 0,1,2,3,4,5,6,7,8,9
a ≠ 0
b ≠ 0
[tex]\bf \overline{ab}-\overline{ba}=45[/tex]
[tex]\bf 10a+b-(10b+a)=45[/tex]
[tex]\bf 10a+b-10b-a=45[/tex]
[tex]\bf 9a-9b=45[/tex]
[tex]\bf 9(a-b)=45~~~\bigg|:9[/tex]
[tex]\bf a-b=5\implies \red{a = 5+b}[/tex]
[tex]\bf b = 1 \implies a = 6\implies \overline{ab} = 61[/tex]
[tex]\bf b =2 \implies a = 7\implies \overline{ab} = 72[/tex]
[tex]\bf b =3 \implies a = 8\implies \overline{ab} = 83[/tex]
[tex]\bf b =4 \implies a =9\implies \overline{ab} = 94[/tex]
[tex]\red{\boxed{\bf~ \overline{ab}~\in~\big\{ 61, 72, 83, 94\big\}~}}[/tex]
