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📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 #### 800Question: If $ x + y = 12 $ and $ x^2 + y^2 = 80 $, find $ x^3 + y^3 $.

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

📌 First, compute $ (x + y)^3 $:

📌 Next, we need $ xy $. Use the identity:

📌 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} $.

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