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Home » = 12^2 - 2ab = 144 - 2ab - wispro

= 12^2 - 2ab = 144 - 2ab - wispro

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Multiply numerator and denominator by the conjugate of the denominator \(2 + \sqrt{5}\):

📌 \[ \frac{3 + \sqrt{5}}{2 - \sqrt{5}} \cdot \frac{2 + \sqrt{5}}{2 + \sqrt{5}} = \frac{(3 + \sqrt{5})(2 + \sqrt{5})}{(2 - \sqrt{5})(2 + \sqrt{5})} \]

📌 First, compute the denominator:

📌 \[ (2)^2 - (\sqrt{5})^2 = 4 - 5 = -1 \]

📌 Now, expand the numerator:

📌 \[ (3)(2) + (3)(\sqrt{5}) + (\sqrt{5})(2) + (\sqrt{5})(\sqrt{5}) = 6 + 3\sqrt{5} + 2\sqrt{5} + 5 = 11 + 5\sqrt{5} \]

📌 \[ \frac{11 + 5\sqrt{5}}{-1} = -11 - 5\sqrt{5} \]

📌 \(\boxed{-11 - 5\sqrt{5}}\)

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