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Home » "BYPASS THE HULK BLOOPER REEL: The Incredible Hulk TV Show Shocks Fans! - Simpleprint

"BYPASS THE HULK BLOOPER REEL: The Incredible Hulk TV Show Shocks Fans! - Simpleprint

📅 March 16, 2026 👤 scraface

Mar 16, 2026

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📌 ight)^2 = rac{625}{2} = 312.5 $. oxed{\dfrac{625}{2}}

📌 Question: Find the number of functions $ f : \mathbb{R} o \mathbb{R} $ such that $ f(a + b) = f(a) + f(b) + ab $ for all real $ a, b $.

📌 Solution: Assume $ f $ is quadratic. Let $ f(x) = px^2 + qx + r $. Substitute into the equation:

📌 Left-hand side: $ f(a + b) = p(a + b)^2 + q(a + b) + r = p(a^2 + 2ab + b^2) + q(a + b) + r $.

📌 Right-hand side: $ f(a) + f(b) + ab = p(a^2 + b^2) + q(a + b) + 2r + ab $.

📌 Equating coefficients:

📌 $ 2pab = ab \Rightarrow 2p = 1 \Rightarrow p = rac{1}{2} $.

📌 $ r = 2r \Rightarrow r = 0 $.

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