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Home » But four points determine a cubic uniquely. - Leaselab

But four points determine a cubic uniquely. - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 u = rac{3 \pm \sqrt{9 - 4}}{2} = rac{3 \pm \sqrt{5}}{2}.

📌 So \( u = rac{3 + \sqrt{5}}{2} \) or \( u = rac{3 - \sqrt{5}}{2} \).

📌 Now recall \( u = rac{x+y}{x-y} \). Let \( r = rac{x}{y} \), assuming \(y

📌 e 0\). Then:

📌 rac{x+y}{x-y} = rac{r+1}{r-1}.

📌 Set this equal to each value of \(u\):

📌 Case 1:** \( rac{r+1}{r-1} = rac{3 + \sqrt{5}}{2} \)

📌 2(r+1) = (3 + \sqrt{5})(r - 1)

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