Question

Aflati cifrele a,b,c(in baza 10) stiind ca ab+bc+ca=abc

Answer 1

$\overline{ab}+\overline{bc}+\overline{ca}=\overline{abc}$
$10a+b+10b+c+10c+a=100a+10b+c$
$11a+11b+11c=100a+10b+c$
$89a-b-10c=0$
observam ca:
b+10c≤99⇒a<2 => a=1
$89-b-10c=0$
89-b trebuie sa fie multiplu de 10 => b=9
$89-9-10c=0 =\ \textgreater \ <strong>c=8</strong>$
Deci a,b,c=1,9,8
19+98+81=198 ok