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can't fight this feeling - Crankk.io

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 12^2 = 80 + 2xy \Rightarrow 144 = 80 + 2xy \Rightarrow 2xy = 64 \Rightarrow xy = 32

📌 Now substitute into the expression for $ x^3 + y^3 $:

📌 x^3 + y^3 = 1728 - 3(32)(12) = 1728 - 1152 = 576

📌 Thus, the answer is $ \boxed{576} $.

📌 Question: A geologist analyzing satellite data finds that the elevation difference between two points in the Himalayas is $ a - b = 6 $ km, and the sum of their squared elevations is $ a^2 + b^2 = 130 $ km². Find $ a^3 - b^3 $.

📌 Solution: We are given $ a - b = 6 $ and $ a^2 + b^2 = 130 $.

📌 a^3 - b^3 = (a - b)(a^2 + ab + b^2)

📌 We already have $ a - b = 6 $ and $ a^2 + b^2 = 130 $. We need $ ab $.

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