Question

cum se rezolvă asta!

Answer 1

$Fie~x~numarul.\\ \\ x:12=cat~rest~5\\ \\ x:15=cat~rest~8\\ \\ \Rightarrow~x=M_{12}+5~si~x=M_{15}+8\\ \\ Daca~adunam~7~la~x~avem:\\ \\ x+7=M_{12}+12=12(t+1),~\forall~t\in~N.\Rightarrow~x+7=M_{12}\\ \\ x+7=M_{15}+15=15(t+1),~\forall~t\in~N~\Rightarrow~x+7=M_{15}\\ \\ Deci,~x+7=cmmmc(12,15)=4*5*3=60.\\ \\ x+7=60\\ \\ \boxed{x=53}$

Answer 2

Fie n numărul căutat.

$\it n:12=a\ \ rest5 \Rightarrow n = 12a+5|_{+7} \Rightarrow n+7 = 12a+12 \Rightarrow n+7\in M_{12}\\ \\ \\n:15=b\ \ rest8 \Rightarrow n = 15b+8|_{+7} \Rightarrow n+7 = 15b+15 \Rightarrow n+7\in M_{15}\\ \\ \\n+7=(12,\ 15) \Rightarrow n+7=60 \Rightarrow n=60-7 \Rightarrow n=53$