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Home » Thus, the circumference of the circle is $ oxed8\sqrt2\pi $. - Dachbleche24

Thus, the circumference of the circle is $ oxed8\sqrt2\pi $. - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 u^2 \cdot u - 5u^2 + 6u = 0 \Rightarrow u^3 - 5u^2 + 6u = 0

📌 So \( u = 0 \), \( u = 2 \), or \( u = 3 \). Since \( v = u^2 \), the corresponding roots are:

📌 \( u = 0 \Rightarrow v = 0 \)

📌 \( u = 2 \Rightarrow v = 4 \)

📌 \( u = 3 \Rightarrow v = 9 \)

📌 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 \( \frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x} \).

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