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Home » You Won’t Believe How Billy Bernthal Conquered Hollywood—Watch the Untold Story! - 500apps

You Won’t Believe How Billy Bernthal Conquered Hollywood—Watch the Untold Story! - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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f(x + y) + f(x - y) = 2f(x) + 2f(y), \quad \forall x, y \in \mathbb{R}
This is known as the **quadratic functional equation**. The general so...
Let $ f(x) = cx^2 $. Then:
f(x+y) + f(x-y) = c(x+y)^2 + c(x-y)^2 = c(x^2 + 2xy + y^2 + x^2 - 2xy...
So it satisfies the equation.
Given $ f(1) = c(1)^2 = 3 \Rightarrow c = 3 $, so $ f(x) = 3x^2 $.
Then $ f(5) = 3 \cdot 25 = \boxed{75} $
Question: A cartographer uses a polynomial $ p(x) $ of degree 3 such t...
Solution: Since $ p(x) $ is a cubic polynomial, when dividing by $ x^4...
p(x) = \text{remainder of } p(x) \div (x^4 - 1) \quad \text{only if }...

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