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Home » x^2 + 2 + \frac1x^2 = 25 \Rightarrow x^2 + \frac1x^2 = 23 - AMAZONAWS

x^2 + 2 + \frac1x^2 = 25 \Rightarrow x^2 + \frac1x^2 = 23 - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Solution: For an equilateral triangle with side length \(s\), the radius \(R\) of the circumscribed circle is given by:

📌 Substituting \(s = 6\), we have:

📌 R = \frac{6}{\sqrt{3}} = 2\sqrt{3}

📌 Therefore, the radius of the circumscribed circle is \(\boxed{2\sqrt{3}}\).Question: A computational biologist is analyzing a dataset of genetic sequences and encounters the equation $ x\sqrt{x} - 5x + 6\sqrt{x} = 0 $. Compute the sum of all real, non-negative roots of this equation.

📌 Solution: Let $ \sqrt{x} = y $, so $ x = y^2 $. Substituting into the equation gives:

📌 y^2 \cdot y - 5y^2 + 6y = 0 \Rightarrow y^3 - 5y^2 + 6y = 0

📌 Factor out $ y $:

📌 y(y^2 - 5y + 6) = 0 \Rightarrow y(y - 2)(y - 3) = 0

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