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📅 March 1, 2026 👤 scraface

Mar 01, 2026

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12^2 = 80 + 2xy \Rightarrow 144 = 80 + 2xy \Rightarrow 2xy = 64 \Right...
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 elevatio...
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 \Right...
Now compute $ a^2 + ab + b^2 = (a^2 + b^2) + ab = 130 + 47 = 177 $.

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