[tex]\displaystyle\it\\\overline{xy}+\overline{yz}+\overline{zx}=121 \Leftrightarrow (10x+y)+(10y+z)+(10z+x)=\\11x+11y+11z=121 |:11 \implies x+y+z=11.\\avand~in~vedere~ca~x<y<z,~avem~cazurile:\\z=8 \implies x+y=3 \implies x=1,~y=2.\\z=7 \implies x+y=4 \implies x=1,~y=3.\\z=6 \implies x+y=5 \implies x=1,~y=4~si~x=2,~y=3.\\z=5 \implies x+y=6 \implies x=2,~y=4.\\si~atat,~celelalte~cazuri~evident~nu~vor~fi~convenabile.[/tex]
