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Aratati ca legea * este asociativa: x*y=x+y+2012

Răspuns :

[tex]\it x*(y*z) =x+(y*z) +2012 =x+y+z+2012+2012= \\ = \it x+y+z +4024\ \ \ (1) \\\;\\ \it (x*y)*z =(x*y)+z+2012 =x+y+2012 +z +2012= \\ =x+y+z+4024\ \ \ (2) \\\;\\ (1), \ (2)\ \Longrightarrow x*(y*z)\ =\ (x*y)*z[/tex]