[tex]\red{\bf \overline{ab} \in \{31, 42, 53, 64, 75, 86,97\}}[/tex]
[tex]\red{\bf \overline{ba} \in \{ 13,24,35,46,57,68,79\}}[/tex]
Explicație pas cu pas:
[tex]\bf \overline{ab}-\overline{ba}=18[/tex]
[tex]\bf a, b - cifre[/tex]
[tex]\bf a\in\{0;1;2;3;4;5;6;7;8;9\}[/tex]
[tex]\bf b\in\{0;1;2;3;4;5;6;7;8;9\}[/tex]
[tex]\bf a, b \neq 0[/tex]
[tex]\bf \overline{ab}-\overline{ba}=18[/tex]
[tex]\bf 10a+b-10b-a=18[/tex]
[tex]\bf 9a-9b=18~~~~~\bigg|:9[/tex]
[tex]\bf a-b=2[/tex]
[tex]\green{\bf\underline{~ a=2+b~}}[/tex]
[tex]\bf \blue{\underline{b = 1}}\Rightarrow a=2+1\Rightarrow \blue{\underline{a=3}}\Rightarrow \pink{\underline{\overline{ab}=31}}~~~\purple{\underline{\overline{ba}=13}}[/tex]
[tex]\bf \blue{\underline{b = 2}}\Rightarrow a=2+2\Rightarrow \blue{\underline{a=4}}\Rightarrow \purple{\underline{\overline{ab}=42}}~~~\pink{\underline{\overline{ba}=24}}[/tex]
[tex]\bf \blue{\underline{b =3}}\Rightarrow a=3+2\Rightarrow \blue{\underline{a=5}}\Rightarrow \pink{\underline{\overline{ab}=53}}~~~\purple{\underline{\overline{ba}=35}}[/tex]
[tex]\bf \blue{\underline{b =4}}\Rightarrow a=4+2\Rightarrow \blue{\underline{a=6}}\Rightarrow \purple{\underline{\overline{ab}=64}}~~~\pink{\underline{\overline{ba}=46}}[/tex]
[tex]\bf \blue{\underline{b =5}}\Rightarrow a=5+2\Rightarrow \blue{\underline{a=5}}\Rightarrow \pink{\underline{\overline{ab}=75}}~~~\purple{\underline{\overline{ba}=57}}[/tex]
[tex]\bf \blue{\underline{b =6}}\Rightarrow a=6+2\Rightarrow \blue{\underline{a=8}}\Rightarrow \purple{\underline{\overline{ab}=86}}~~~\pink{\underline{\overline{ba}=68}}[/tex]
[tex]\bf \blue{\underline{b =7}}\Rightarrow a=7+2\Rightarrow \blue{\underline{a=9}}\Rightarrow \pink{\underline{\overline{ab}=97}}~~~\purple{\underline{\overline{ba}=79}}[/tex]
[tex]\bf b =8\Rightarrow a=8+2\Rightarrow a=10~~Nu~ convine ~deoarece ~a = cifra[/tex]
[tex]\red{\boxed{\bf \overline{ab} \in \{31, 42, 53, 64, 75, 86,97\}}}[/tex]
[tex]\red{\boxed{\bf \overline{ba} \in \{ 13,24,35,46,57,68,79\}}}[/tex]
[tex]==pav38==[/tex]
