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does target price match amazon - SUpost

📅 July 5, 2026 👤 scraface

Jul 05, 2026

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📌 To find the minimum value of \( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \), given \( x + y + z = 6 \), use the AM-HM inequality:

📌 \frac{x + y + z}{3} \geq \frac{3}{\frac{1}{x} + \frac{1}{y} + \frac{1}{z}}

📌 Substitute \( x + y + z = 6 \):

📌 \frac{6}{3} \geq \frac{3}{\frac{1}{x} + \frac{1}{y} + \frac{1}{z}}

📌 \geq \frac{3}{\frac{1}{x} + \frac{1}{y} + \frac{1}{z}}

📌 \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \geq \frac{3}{2}

📌 Equality holds when \( x = y = z \). Since \( x + y + z = 6 \), set \( x = y = z = 2 \).

📌 \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = \frac{3}{2}

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