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Home » Why Every Coffee Lover’s Basement Needs This Stylish Ceramic Mug! - American Beagle Club

Why Every Coffee Lover’s Basement Needs This Stylish Ceramic Mug! - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Area = πr² = 3.14 × 5² = 3.14 × 25 = 78.5 square meters.

📌 #### 78.5Question: Let $ a $ and $ b $ be complex numbers such that $ a^2 + b^2 = 1 $ and $ ab = \frac{1}{2} $. Find $ |a^4 + b^4| $.

📌 Solution: We are given that $ a^2 + b^2 = 1 $ and $ ab = \frac{1}{2} $. We are to find $ |a^4 + b^4| $.

📌 We start by using the identity:

📌 a^4 + b^4 = (a^2 + b^2)^2 - 2a^2b^2

📌 We already know $ a^2 + b^2 = 1 $ and $ ab = \frac{1}{2} $, so

📌 a^2b^2 = (ab)^2 = \left(\frac{1}{2}\right)^2 = \frac{1}{4}

📌 Substituting into the identity:

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