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Home » The Hidden Way to Say Hi in German That Every Local Will Notice! - Upplift

The Hidden Way to Say Hi in German That Every Local Will Notice! - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 Solution: We apply the **Cauchy-Schwarz inequality** in the Engel form (also known as Titu’s Lemma):

📌 \frac{a_1^2}{b_1} + \frac{a_2^2}{b_2} + \frac{a_3^2}{b_3} \ge \frac{(a_1 + a_2 + a_3)^2}{b_1 + b_2 + b_3}

📌 But our expression is $ \frac{1}{x} + \frac{4}{y} + \frac{9}{z} = \frac{1^2}{x} + \frac{2^2}{y} + \frac{3^2}{z} $

📌 Apply Titu’s Lemma:

📌 \frac{1^2}{x} + \frac

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f(2) + f(0) = 4 \quad \text{(1)}
Now plug in $ a = 0, b = 1 $:
f(1) + f(-1) = 2f(0) + 2f(1) \Rightarrow 1 + f(-1) = 2f(0) + 2 \Righta...
Now plug in $ a = 1, b = 0 $:
f(1) + f(1) = 2f(1) + 2f(0) \Rightarrow 2 = 2 + 2f(0) \Rightarrow f(0)...
Substitute $ f(0) = 0 $ into equation (1):
f(2) + 0 = 4 \Rightarrow f(2) = \boxed{4}
Question: Find the area enclosed by the graph of $ |x| + |y| = 4 $.
Solution: The equation $ |x| + |y| = 4 $ represents a diamond (rhombus...
The diamond has diagonals of length 8 (horizontal) and 8 (vertical), s...

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