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Home » بما أن \( 625 = 625 \)، فإن المثلث هو مثلث قائم الزاوية. - Dyverse

بما أن \( 625 = 625 \)، فإن المثلث هو مثلث قائم الزاوية. - Dyverse

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Solution: We are given that $ f(x) = ax^3 + bx^2 + cx + d $ and the values:

📌 f(1) = 15,\quad f(2) = 30,\quad f(3) = 45,\quad f(4) = 60

📌 We observe that the values increase linearly: $ f(x) = 15x $ fits all given points.

📌 Since $ f(x) $ is a cubic polynomial and agrees with a linear function at four points, and a cubic can only differ from a linear function by a cubic term that vanishes at those points, define:

📌 f(x) = 15x + k(x - 1)(x - 2)(x - 3)(x - 4)

📌 But since $ f(x) $ is only cubic, the quartic term must vanish, so $ k = 0 $. Therefore:

📌 f(x) = 15x

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