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Home » Love Thy Neighbor Verse Exposed—This Bible Skip Every Closet Mystery! - Silent Sales Machine

Love Thy Neighbor Verse Exposed—This Bible Skip Every Closet Mystery! - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Question: A mammalogist models the population of a species using the functional equation $ h(x + y) = h(x) + h(y) + xy $ for all real $ x, y $. Find all functions $ h: \mathbb{R} o \mathbb{R} $.

📌 Solution: Assume $ h(x) = ax^2 + bx + c $. Substitute into the equation:

📌 a(x + y)^2 + b(x + y) + c = ax^2 + bx + c + ay^2 + by + c + xy.

📌 Expand left side: $ a(x^2 + 2xy + y^2) + b(x + y) + c = ax^2 + 2a xy + a y^2 + b x + b y + c $.

📌 Right side: $ ax^2 + ay^2 + bx + by + 2c + xy $.

📌 Equate coefficients:

📌 $ 2a = 1 $ (for $ xy $): $ a = rac{1}{2} $.

📌 $ 2c = c $: $ c = 0 $.

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