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Home » Avatar Season 3 Shakes the Universe: Don’t Miss This Must-See Climax! - Abbey Badges

Avatar Season 3 Shakes the Universe: Don’t Miss This Must-See Climax! - Abbey Badges

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📝 Recent Posts

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...
Question: Let $ h(x) $ be a polynomial such that $ h(x^3 + 1) = x^6 +...
Solution: Observe that the right-hand side is $ (x^3 + 1)^2 + 2 $. How...

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