Question

Va rog sa ma ajutati: 2012+(2012*2013-2014*2011)
Raspunsul este 2014, dar cum ajungi la el fara sa faci inmultirile? Multumesc!

Answer 1

2012+ ( 2012*2013 - 2014*2011)

n*(n+1) - (n+2)(n-1)= n²+n -( n²+n-2)=n²+n-n²-n+2= 2; unde n= 2012

deci⇒

 ( 2012*2013 - 2014*2011)= 2

⇒
2012+ ( 2012*2013 - 2014*2011)= 2012+2=2014

Answer 2

   
[tex]2012+(2012\times 2013-2014 \times 2011) = \\ 2012+2012\times 2013-2014 \times 2011 = \\ 2012+(2011+1)(2011+2)-(2011+3)2011 = \\ 2012+(2011^2 +2011 + 2\times 2011 +2)-(2011^2+3 \times 2011) = \\ 2012+(2011^2 + 3\times 2011 +2)-(2011^2+3 \times 2011) = \\ 2012+\underline{2011^2} + \underline{\underline{3\times 2011}} +2-\underline{2011^2}-\underline{\underline{3 \times 2011}} =2012+2 = \boxed{2014} [/tex]