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Home » \(racddx[-5x^2] = -10x\), - High Altitude Science

\(racddx[-5x^2] = -10x\), - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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Only \(x \approx 6.27\) is valid since \(x^2 - 5x > 0\).
#### 6.27Question: Let $ x, y, z $ be positive real numbers such that...
Solution: To minimize the expression
S = \frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x},
given that $ x + y + z = 1 $ and $ x, y, z > 0 $, we apply the **Cauch...
Since $ x + y + z = 1 $, we substitute into the inequality:
S \geq 1.
To check if this bound is achievable, consider the equality condition...
Let this common value be $ k $. Then,
\frac{x^2}{y} = \frac{y^2}{z} \Rightarrow x^2 z = y^3, \quad \frac{y^2...

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