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IMAS 2014–2015 — Junior — Round 2 Question 12

IMAS · IMAS 2014–2015 — Junior — Round 2

Question 12

Let $k$ be a non-zero integer such that the equation $x+\frac{9k^2-81}{x}=10k$ has two distinct integer roots. What is the difference when the smaller root is subtracted from the larger one?