Question:medium
Let \( u + v + w = 3 \), \( u, v, w \in \mathbb{R} \) and \( f(x) = ux^2 + vx + w \) be such that \( f(x + y) = f(x) + f(y) + xy \) for all \( x, y \in \mathbb{R} \). Then \( f(1) \) is equal to:
Let \( u + v + w = 3 \), \( u, v, w \in \mathbb{R} \) and \( f(x) = ux^2 + vx + w \) be such that \( f(x + y) = f(x) + f(y) + xy \) for all \( x, y \in \mathbb{R} \). Then \( f(1) \) is equal to:
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Always compare the coefficients carefully when matching expansions. Special attention to cross terms like \(xy\) is key!
Updated On: Nov 28, 2025
- \( \frac{5}{2} \)
- \( \frac{1}{2} \)
- \( \frac{1}{\sqrt{2}} \)
- \( 3 \)