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Home » Since \( x \) must be a whole number, check calculations: - AMAZONAWS

Since \( x \) must be a whole number, check calculations: - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 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:

📌 f(x) = x^3.

📌 f(2) = 2^3 = 8.

📌 Even though the problem states "cubic polynomial," and $ x^3 $ is cubic with integer coefficients, this fits. Therefore, the answer is:

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x^3 + rac{1}{x^3} = 3^3 - 3 \cdot 3 = 27 - 9 = 18
oxed{18}
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لنفترض أن العرض هو \( w \). إذن، الطول هو \( 2w \).
2(\text{الطول} + \text{العرض}) = 36
2(2w + w) = 36
6w = 36
بحل المعادلة لإيجاد \( w \):
لذلك، الطول هو \( 2w = 12 \).
تُعطى المساحة \( A \) بالصيغة:

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