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Home » Why Everyone’s Obsessed with This Pink Champagne—You Must Add It to Your Routine! - Simpleprint

Why Everyone’s Obsessed with This Pink Champagne—You Must Add It to Your Routine! - Simpleprint

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 rac{a + b + c}{3} \geq rac{3}{rac{1}{a} + rac{1}{b} + rac{1}{c}} \Rightarrow rac{1}{3} \geq rac{3}{rac{1}{a} + rac{1}{b} + rac{1}{c}}

📌 Taking reciprocals (since all terms are positive):

📌 rac{1}{a} + rac{1}{b} + rac{1}{c} \geq 9

📌 Equality occurs when $ a = b = c = rac{1}{3} $. Thus, the minimum value is:

📌 Question: Let $ h(x) $ be a polynomial such that $ h(x^3 + 1) = x^6 + 3x^3 + 3 $. Find $ h(x^3 - 1) $.

📌 Solution: Observe that the right-hand side is $ (x^3 + 1)^2 + 2 $. However, we can directly write:

📌 h(x^3 + 1) = (x^3 + 1)^2 + 2 \Rightarrow h(u) = u^2 + 2

📌 Then, substitute $ u = x^3 - 1 $:

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