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2001 IMO Shortlist Problems/N2

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Problem

Consider the system x + y = z + u, 2xy & = zu. Find the greatest value of the real constant m such that m \leq x/y for any positive integer solution (x,y,z,u) of the system, with x \geq y.

Solution

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Resources

Looking for a challenging algebra text? Preparing for MATHCOUNTS or the AMC exams?
Check out Art of Problem Solving's Introduction to Algebra by Richard Rusczyk.
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