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will so you think you can dance - Malaeb

📅 May 2, 2026 👤 scraface

May 02, 2026

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Solution: We are given $ p + q = 5 $ and $ pq = 6 $. We use the identi...
p^3 + q^3 = (p + q)^3 - 3pq(p + q)
p^3 + q^3 = 5^3 - 3 \cdot 6 \cdot 5 = 125 - 90 = 35
Question: Let $ a $, $ b $, and $ c $ be positive real numbers such th...
Solution: We are to minimize $ rac{1}{a} + rac{1}{b} + rac{1}{c} $...
By the AM-HM inequality:
rac{a + b + c}{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 val...

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