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Home » 2\sin^2 z - 3\sin z + 1 = 0 - ToelettAPP

2\sin^2 z - 3\sin z + 1 = 0 - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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Let us define $ a = rac{x}{y} $, $ b = rac{y}{z} $, and $ c = rac{z...
abc = rac{x}{y} \cdot rac{y}{z} \cdot rac{z}{x} = 1.
We are to minimize
a + b + c - \log\left(rac{x}{z} + rac{z}{x}
ight) = a + b + c - \log\left(rac{1}{b} + b
since $ rac{x}{z} = rac{x}{y} \cdot rac{y}{z} = ac = rac{1}{b} $,...
a + b + c - \log\left(b + rac{1}{b}
Since $ abc = 1 $, we can assume $ a = rac{x}{y} $, $ b = rac{y}{z}...
a + b + c \geq 3\sqrt[3]{abc} = 3.
Equality occurs when $ a = b = c = 1 $, i.e., when $ x = y = z $.

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