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Home » نطرح 5 من كلا الجانبين: - Dachbleche24

نطرح 5 من كلا الجانبين: - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 f(g(5)) = (2\sqrt{2})^2 + 2(2\sqrt{2}) + 1 = 8 + 4\sqrt{2} + 1 = 9 + 4\sqrt{2}

📌 \boxed{9 + 4\sqrt{2}}

📌 Question:** A philosopher of science is analyzing a relationship where \( a + b = 10 \) and \( a^2 + b^2 = 58 \). Determine \( a^3 + b^3 \).

📌 Start by using the identity for the sum of cubes:

📌 a^3 + b^3 = (a+b)(a^2 - ab + b^2)

📌 We know \( a + b = 10 \) and \( a^2 + b^2 = 58 \). Use the identity:

📌 a^2 + b^2 = (a+b)^2 - 2ab

📌 = 10^2 - 2ab \implies 58 = 100 - 2ab \implies 2ab = 42 \implies ab = 21

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