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📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 Next 48 hours: 35% of 10,800 = 3,780 tons dispersed

📌 Find all possible functions $ f $ satisfying this equation.

📌 Step 1: Plug in $ x = 0 $, $ y = 0 $.

📌 Thus, $ f(-y) = f(y) $, so $ f $ is even.

📌 Step 3: Use symmetry and known techniques.

📌 The given equation resembles the functional equation for quadratic forms. Recall that functions satisfying

📌 are known to be quadratic under mild regularity conditions (typically implied in olympiad problems unless otherwise stated).

📌 But simpler: assume $ f $ satisfies (1). Define $ g(x) = f(x) $. We already know evenness and $ f(0) = 0 $.

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