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Home » Solution: We are given $ x + y = 12 $ and $ x^2 + y^2 = 80 $. - jntua results

Solution: We are given $ x + y = 12 $ and $ x^2 + y^2 = 80 $. - jntua results

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Unless the "largest" is not 729, but the sequence starts with capacity larger? No.

📌 Alternative: The first bottle used has capacity 729, but we only fill part. But question says "the largest", implying relative.

📌 Given ambiguity, assume standard geometric series: total volume to be distributed in a sequence of bottles with capacities in geometric progression: \(a, a/2, a/4, \dots\)

📌 But total is \(S = a / (1 - r) = a / (1 - 1/2) = 2a\)

📌 Set \(2a = 729\) → \(a = 364.5\)

📌 Then bottles: 364.5, 182.25, 91.125, 45.5625, 22.78125, 11.390625, 5.6953125, 2.84765625, 1.423828125, 0.7119140625, ...

📌 Sum after n terms: \(S_n = a(1 - (1/2)^n)/(1 - 1/2) = 2a(1 - 2^{-n})\)

📌 Set \(2a = 729\), so \(S_n = 729(1 - 2^{-n})\)

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