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📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 Thus \( h(x) = rac{2}{3}x^3 + rac{4}{3}x + 2 \)

📌 Now compute \( h(0) = 0 + 0 + 2 = 2 \)

📌 Question: A historian of science analyzing Newtonâs early work considers the equation \( v\sqrt{v} - 5v + 6\sqrt{v} = 0 \), where \( v > 0 \) represents velocity-related magnitude. Find the sum of all real roots.

📌 Solution: We are given the equation:

📌 v\sqrt{v} - 5v + 6\sqrt{v} = 0, \quad v > 0

📌 Note that \( v\sqrt{v} = v^{3/2} \) and \( \sqrt{v} = v^{1/2} \). Let \( u = \sqrt{v} \), so \( v = u^2 \), and \( v^{3/2} = u^3 \). Substitute:

📌 u^3 - 5u^2 + 6u = 0

📌 u(u^2 - 5u + 6) = 0

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