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Home » km = 1,500,000 cm - Dachbleche24

km = 1,500,000 cm - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 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 $.

📌 6^2 = 130 - 2ab \Rightarrow 36 = 130 - 2ab \Rightarrow 2ab = 94 \Rightarrow ab = 47

📌 Now compute $ a^2 + ab + b^2 = (a^2 + b^2) + ab = 130 + 47 = 177 $.

📌 a^3 - b^3 = 6 \cdot 177 = 1062

📌 Thus, the answer is $ \boxed{1062} $.

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