Simple Maths 4 -3-
2007-12-26 7:57 am
Let A be a set containing only positive integers, and for any elements x and y in A, |x-y| > or =xy/25. Determine at most how many elements A may contain.
回答 (1)
2007-12-26 7:51 pm
✔ 最佳答案
for x>yx-y>xy/25
25(x-y)>xy
25x-xy-25y>0
x(25-y)-25y>0
x(25-y)-25y+y^2-y^2>0
(x-y)(25-y)-y^2>0
(x-y)(25-y)>0
y<25
for x
xy/25
similarly,x<25
so there are 24 integer in set A
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