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Home » Perimeter = \( 2(w + 2w) = 36 \) - Feedz API

Perimeter = \( 2(w + 2w) = 36 \) - Feedz API

📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 \( u = 0 \Rightarrow v = 0 \)

📌 \( u = 2 \Rightarrow v = 4 \)

📌 \( u = 3 \Rightarrow v = 9 \)

📌 All roots are non-negative, so valid. The sum of the roots is \( 0 + 4 + 9 = 13 \).

📌 Thus, the sum is \( \boxed{13} \).

📌 Question: Let \( x, y, z \) be positive real numbers such that \( x + y + z = 3 \). Find the minimum value of \( \frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x} \).

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

📌 \frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x} \geq \frac{(x + y + z)^2}{y + z + x} = \frac{3^2}{3} = 3

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