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Home » Breakfast for Dinner: The Secret Trick to Better Health & Bigger Creativity! - Dachbleche24

Breakfast for Dinner: The Secret Trick to Better Health & Bigger Creativity! - Dachbleche24

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Thus, the value is \(\boxed{13}\).

📌 Question: A theoretical physicist models a quantum state where the sum of two energy levels \( E_1 \) and \( E_2 \) is 12 units, and \( E_1^2 + E_2^2 = 80 \). Find \( E_1^3 + E_2^3 \).

📌 E_1 + E_2 = 12, \quad E_1^2 + E_2^2 = 80

📌 E_1^3 + E_2^3 = (E_1 + E_2)^3 - 3E_1E_2(E_1 + E_2)

📌 First, compute \( (E_1 + E_2)^3 = 12^3 = 1728 \)

📌 Next, find \( E_1E_2 \) using:

📌 = 80 + 2E_1E_2 \Rightarrow 2E_1E_2 = 64 \Rightarrow E_1E_2 = 32

📌 E_1^3 + E_2^3 = 1728 - 3(32)(12) = 1728 - 1152 = 576

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