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Home » x^2 + y^2 \geq 2xy \Rightarrow racx^2 + y^2xy \geq 2, - Dachbleche24

x^2 + y^2 \geq 2xy \Rightarrow racx^2 + y^2xy \geq 2, - Dachbleche24

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Let \( a \) and \( b \) be complex numbers such that \( a + b = 4 \) and \( a^2 + b^2 = 10 \). Find \( |a - b| \).

📌 \( a + b = 4 \)

📌 \( a^2 + b^2 = 10 \)

📌 We use the identity:

📌 Substitute:

📌 4^2 = 10 + 2ab \Rightarrow 16 = 10 + 2ab \Rightarrow 2ab = 6 \Rightarrow ab = 3

📌 Now compute \( |a - b| \). Note:

📌 |a - b|^2 = (a - b)(\overline{a} - \overline{b}) = |a|^2 - a\overline{b} - \overline{a}b + |b|^2

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