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= \( 2 \times 3 \times 5 \) - Treasure Valley Movers

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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Solution: We are to minimize the expression
subject to $ x + y + z = 1 $, with $ x, y, z > 0 $.
Apply the **Cauchy-Schwarz Inequality** in the following form:
\left( \frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x} \right)(y + z + x...
Since $ x + y + z = 1 $, we have:
\left( \frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x} \right)(1) \geq 1...
\frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x} \geq 1
Equality holds when $ \frac{x}{y} = \frac{y}{z} = \frac{z}{x} $, which...
Check the expression at $ x = y = z = \frac{1}{3} $:
\frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x} = 3 \cdot \frac{(1/3)^2}...

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