Question

Aflati numerele ab și ba care verificarea
egalitatea: ab- ba= 18

Answer 1

Răspuns:

..............................

Answer 2

$\red{\bf \overline{ab} \in \{31, 42, 53, 64, 75, 86,97\}}$

$\red{\bf \overline{ba} \in \{ 13,24,35,46,57,68,79\}}$

Explicație pas cu pas:

$\bf \overline{ab}-\overline{ba}=18$

$\bf a, b - cifre$

$\bf a\in\{0;1;2;3;4;5;6;7;8;9\}$

$\bf b\in\{0;1;2;3;4;5;6;7;8;9\}$

$\bf a, b \neq 0$

$\bf \overline{ab}-\overline{ba}=18$

$\bf 10a+b-10b-a=18$

$\bf 9a-9b=18~~~~~\bigg|:9$

$\bf a-b=2$

$\green{\bf\underline{~ a=2+b~}}$

$\bf \blue{\underline{b = 1}}\Rightarrow a=2+1\Rightarrow \blue{\underline{a=3}}\Rightarrow \pink{\underline{\overline{ab}=31}}~~~\purple{\underline{\overline{ba}=13}}$

$\bf \blue{\underline{b = 2}}\Rightarrow a=2+2\Rightarrow \blue{\underline{a=4}}\Rightarrow \purple{\underline{\overline{ab}=42}}~~~\pink{\underline{\overline{ba}=24}}$

$\bf \blue{\underline{b =3}}\Rightarrow a=3+2\Rightarrow \blue{\underline{a=5}}\Rightarrow \pink{\underline{\overline{ab}=53}}~~~\purple{\underline{\overline{ba}=35}}$

$\bf \blue{\underline{b =4}}\Rightarrow a=4+2\Rightarrow \blue{\underline{a=6}}\Rightarrow \purple{\underline{\overline{ab}=64}}~~~\pink{\underline{\overline{ba}=46}}$

$\bf \blue{\underline{b =5}}\Rightarrow a=5+2\Rightarrow \blue{\underline{a=5}}\Rightarrow \pink{\underline{\overline{ab}=75}}~~~\purple{\underline{\overline{ba}=57}}$

$\bf \blue{\underline{b =6}}\Rightarrow a=6+2\Rightarrow \blue{\underline{a=8}}\Rightarrow \purple{\underline{\overline{ab}=86}}~~~\pink{\underline{\overline{ba}=68}}$

$\bf \blue{\underline{b =7}}\Rightarrow a=7+2\Rightarrow \blue{\underline{a=9}}\Rightarrow \pink{\underline{\overline{ab}=97}}~~~\purple{\underline{\overline{ba}=79}}$

$\bf b =8\Rightarrow a=8+2\Rightarrow a=10~~Nu~ convine ~deoarece ~a = cifra$

$\red{\boxed{\bf \overline{ab} \in \{31, 42, 53, 64, 75, 86,97\}}}$

$\red{\boxed{\bf \overline{ba} \in \{ 13,24,35,46,57,68,79\}}}$

$==pav38==$