Hey! Combinatorics + Inequality!

There are at most \(2009\) balls, consisting of white balls and blue balls at random inside a locker. If two balls are taken randomly without returning, it is known that the probability which the two balls are both white or both blue are \(\frac{1}{2}\). Whay is the maximum number of white ball might be in the drawer so that the statement about the probability of still holds?

Details and Assumption! This problem is not original. I take it from OSN Matematika SMA year 2009 Problem 5 Day 2 (English: Senior High School National Science Olympiad in Mathematics Field yr. 2009 Problem 5 Day 2)

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