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Aratati ca numarul a=2017+2x(1+2+...+2016) este patrat perfect.

Răspuns :

a = 2017 + 2·(1 + 2 + ...+ 2016)

a = 2017 + 2·2016·2017 : 2

a = 2017 + 2016·2017

a = 2017·(1 + 2016)

a = 2017·2017

a = 2017²

a=2017+2x(1+2+...+2016) =

= 2017+2* (2016*2017)/2 =

= 2017 *( 1+2016) = 2017*2017 = 2017²