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Aratati ca numarul a=2012 la puterea 2 +2012+2013 este patrat perfect

Răspuns :

= 2012 ( 2012 + 1 ) +2013 = 2012 ·2013 + 2013 = 2013 ·( 2012 +1) =
= 2013· 2013 = 2013² patrat perfect
[tex]a=2012^2+2012+2013= \\ \\ =2012(2012+1)+2013= \\ \\ =2012 \cdot 2013 + 2013= \\ \\ =2013 (2012 +1)= \\ \\ =2013 \cdot 2013= \\ \\ =2013^2-patrat~perfect[/tex]