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Home » \[ c^2 = a^2 + b^2 \] - DNSFLEX

\[ c^2 = a^2 + b^2 \] - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Let $ x = \frac{d}{a} $, $ x^2 = \frac{7}{9} \Rightarrow x = \pm \frac{\sqrt{7}}{3} $. Try $ x = \frac{\sqrt{7}}{3} $:

📌 \frac{1 + \frac{\sqrt{7}}{3}}{1 - \sqrt{7}} = \frac{\frac{3 + \sqrt{7}}{3}}{1 - \sqrt{7}} = \frac{3 + \sqrt{7}}{3(1 - \sqrt{7})}.

📌 Numerator: $ (3 + \sqrt{7})(1 + \sqrt{7}) = 3 + 3\sqrt{7} + \sqrt{7} + 7 = 10 + 4\sqrt{7} $.

📌 Denominator: $ 3(1 - 7) = 3(-6) = -18 $.

📌 So ratio: $ \frac{10 + 4\sqrt{7}}{-18} = -\frac{5 + 2\sqrt{7}}{9} $.

📌 Now $ x = -\frac{\sqrt{7}}{3} $:

📌 \frac{1 - \frac{\sqrt{7}}{3}}{1 + \sqrt{7}} = \frac{\frac{3 - \sqrt{7}}{3}}{1 + \sqrt{7}} = \frac{3 - \sqrt{7}}{3(1 + \sqrt{7})}.

📌 Multiply by $ 1 - \sqrt{7} $:

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