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Home » \frac63 \geq \frac3\frac1x + \frac1y + \frac1z - jntua results

\frac63 \geq \frac3\frac1x + \frac1y + \frac1z - jntua results

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 5Question: Let $ f(x) $ represent the energy output (in megawatts) of a wind turbine at wind speed $ x $ (in meters per second), modeled by a cubic polynomial. Suppose $ f(3) = 27 $, $ f(4) = 64 $, $ f(5) = 125 $, and $ f(6) = 216 $. Determine $ f(2) $, assuming the polynomial has integer coefficients.

📌 Solution: We are given that $ f(x) $ is a cubic polynomial such that:

📌 f(3) = 27,\quad f(4) = 64,\quad f(5) = 125,\quad f(6) = 216.

📌 Notice that:

📌 = 3^3,\quad 64 = 4^3,\quad 125 = 5^3,\quad 216 = 6^3.

📌 This suggests that $ f(n) = n^3 $ for $ n = 3, 4, 5, 6 $. However, $ f(x) $ is a cubic polynomial, and $ x^3 $ is already a cubic polynomial. Since a cubic is uniquely determined by four points, and $ f(n) = n^3 $ satisfies all four conditions, we conclude:

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