2006 Romanian NMO Problems/Grade 9/Problem 1
Find the maximal value of
where , .
If y is negative, then is also negative, so we want .
where . Let's see what happens when a gets large:
As a gets large, the fraction gets small, therefore maximizing . But when a gets small(up to 2), the fraction gets bigger, and therefore lessens .
Therefore, the maximum value of is when x=1 and y=0, which is 2.