Question

aflati nr. naturale de forma abc, stiind ca abc-ab-c=486

Answer 1

   
[tex]\displaystyle \\ \overline{abc}-\overline{ab}-\overline{c}=486 \\ \\ 100a+10b+c -(10a+b) -c = 486 \\ \\ 100a+10b+c -10a-b -c = 486 \\ \\ 90a +9b = 486 \\ \\ 9(10a+b)=486 \\ \\ 9\times \overline{ab} = 486 \\ \\ \overline{ab} = \frac{486}{9} = 54 \\ \\ \\ \Longrightarrow~~\boxed{a=5;~~b=4~~\text{si } ~c \in \{0;~1;~2;~3;~4;~5;~6;~7;~8;~9\} }\\ \\ \Longrightarrow~~\boxed{\overline{abc} \in \{540;~541;~542;~543;~544;~545;~546;~547;~548;~549\}}[/tex]