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📰 Question: Let $ a $, $ b $, and $ c $ be positive real numbers such that $ a + b + c = 1 $. Find the minimum value of $ rac{1}{a} + rac{1}{b} + rac{1}{c} $. 📰 Solution: We are to minimize $ rac{1}{a} + rac{1}{b} + rac{1}{c} $ under the constraint $ a + b + c = 1 $ with $ a, b, c > 0 $. 📰 By the AM-HM inequality: