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Home » These Movie Villains Are So Evil, Hollywood Still Can’t Get Through Them! - inBeat

These Movie Villains Are So Evil, Hollywood Still Can’t Get Through Them! - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 5Question: Let $ x, y, z $ be positive real numbers such that $ x + y + z = 1 $. Find the minimum value of

📌 However, note that $ x > y $ must hold for the expression to be defined (since $ x - y

📌 Now, we analyze whether the minimum value of 2 is achievable. For $ u +

📌 eq 1 $, and the expression is strictly greater than 2. We now consider the behavior of $ A = u +

📌 But we must also ensure $ z > 0 $, i.e., $ x + y < 1 $. This does not directly affect the minimum of $ A $, which depends only on $ x $ and $ y $.

📌 Thus, the infimum is 2, but it is never attained for positive $ x, y $ with $ x

📌 e y $. However, since the domain is open (positive reals, $ x

📌 e y $), the minimum is not achieved, but the greatest lower bound is 2.

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