[tex]Dac\u{a}\; x+y+z=11\;atunci,\\
(1)...\;\overline{xy}+\overline{yz}+\overline{zx}=p\u{a}trat\;perfect \\
\Leftrightarrow\;10x+y \;+\;10y+z\;+\;10z+x=11(\underbrace{x+y+z}_{=11})=11^2\\
(2)...\;Dac\u{a}\;x;y;z\; sunt\;nume\;consecutive\;atunci\;\\
y=x+1\;\c{s}i\;z=x+2 \;atunci\;,\\
\overline{xy}+\overline{yz}+\overline{zx}=\\
=10x+(x+1)\;+\;10(x+1)+(x+2)\;+\;10(x+2)+x=\\
=10x+10+10x+10+x+2+10x+20+x=32x+42\ne{p.p.
[/tex]
