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Home » Solve for \( x \) in the equation \( 2x^2 - 3x - 5 = 0 \). - AMAZONAWS

Solve for \( x \) in the equation \( 2x^2 - 3x - 5 = 0 \). - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Now use the identity:

📌 = |z|^2 + |w|^2 + 2 \operatorname{Re}(z \overline{w}) = 26 + 2 \cdot 5 = 26 + 10 = 36? \quad ext{Wait, contradiction.}

📌 Wait â correction:

📌 From identity:

📌 Substitute known values:

📌 = 26 + 2 \operatorname{Re}(z \overline{w}) \Rightarrow 2 \operatorname{Re}(z \overline{z}) = 20 - 26 = -6 \Rightarrow \operatorname{Re}(z \overline{w}) = -3

📌 But this contradicts $ \operatorname{Re}(z \overline{w}) = 5 $ from (2). So we must reevaluate:

📌 Wait â there is an error in interpretation. The expression $ z \overline{w} + \overline{z} w = 2 \operatorname{Re}(z \overline{w}) $, and this is given as 10, so $ \operatorname{Re}(z \overline{w}) = 5 $.

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