Question

aflati toate numerele de abc stiind ca abc -ab-c=153

Answer 1

Numerele in cauza scrise in baza 10 au forma:
[tex] (abc)^{-} =100*a+10*b+c \\ (ab)^{-}=10*a+b \\ (c)^{-} =c[/tex]
Egalitatea din enunț devine:
[tex]100*a+10*b+c-(10*a+b)-c=153 \ \textless \ =\ \textgreater \ \\ 100*a+10*b-10*a-b=153 \ \textless \ =\ \textgreater \ 90*a+9*b=153 \ \textless \ =\ \textgreater \ \\ 9*(10*a+b)=9*17 \ |:9 =\ \textgreater \ 10*a+b=17 \ \textless \ =\ \textgreater \ \\ 10*a=17-b\ \textless \ 20 =\ \textgreater \ 10*a\ \textless \ 20=\ \textgreater \ a\ \textless \ 2=\ \textgreater \ a \in [0,1] \\ Daca \ a=0 =\ \textgreater \ 10*0=17-b=\ \textgreater \ b=17 -\ \textgreater \ \ absurd \ pentru \ ca \ b \leq 9 \\ Asadar \ a=1 =\ \textgreater \ 10*1+b=17 \ \textless \ =\ \textgreater \ b+10=17 \ \textless \ =\ \textgreater \ \\ b=17-10=\ \textgreater \ b=7 \\ Am \ obtinut \ astfel: \\ (17c)^{-} - 17 - c=153 \ \textless \ =\ \textgreater \ (17c)^{-} -c =153+17 \ \textless \ =\ \textgreater \ \\ (17c)^{-}-c=170 \ \textless \ =\ \textgreater \ (17c)^{-}-c=170-0=\ \textgreater \ c=0 \\ In \ concluzie \ numarul \ cautat \ este: \ 170 [/tex]

Sper sa fie destul de explicita rezolvarea problemei.
$(abc)^{-}$ - reprezinta numarul abc scris cu bara deasupra.