Question

Matematica. Cls. a VIII-a. Rezolva ecuatia
(x+1)/2 +(x+2)/3 + ... +(x+2012)/2013 =2012. (problema Mate2000 consolidare)

Answer 1

relatia e echivalenta cu:
x/2+x/3+...+x/2013+1/2+2/3+...+2012/2013=2012
x(1/2+1/3+...+1/2013)+1-1/2+1-1/3+....+1-1/2013=2012
x(1/2+1/3+...+1/2013)+2012-(1/2+1/3+...+1/2013)=2012
(x-1)(1/2+1/3+...+1/2013)=0
x-1=0    sau 1/2+1/3+...+1/2013=0(fals)
rezulta ca x=1