11Suppose there are 7 reals - x1,x2,x3...x7
tan-1xi=ai
Since a1-a7≤180 deg, there must exist some pair whose difference is less than 30 deg.
Thus proved.
This one is another of those which are very common olympiad type.. but i think are very important for jee aspirants too...
if there are 7 distinct real numbers, show that there will be atleast 2 of them say x,y are such that
0 < x-y1+xy < 1√3
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2 Answers
11
62yes soumik...
I hope you have implied that you have ordered them in ascending order... :)