Question

determinați numerele naturale abc care verifica relația abc-ab-c=207​

Answer 1

 

$\displaystyle\bf\\\overline{abc}-\overline{ab}-\overline{c}=207\\\\100a+10b+c-(10a+b)-c=207\\\\100a+10b+c-10a-b-c=207\\\\100a-10a+10b-b+c-c=207\\\\90a+9b=207\\\\9(10a)+9b=207~~~\Big|:9\\\\10a+b=23\\\\\overline{ab}=23\\\\\implies~\boxed{\bf~a=2;~~b=3;~~c\in\{0;~1;~2;~3;~4;~5;~6;~7;~8;~9\}}$

$\boxed{\bf\overline{abc}\in\{230;~231;~232;~233;~234;~235;~236;~237;~238;~239\}}$

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