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Home » Therefore, the radius of the sphere is 6 units. - Upplift

Therefore, the radius of the sphere is 6 units. - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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

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