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Home » Check if this is greater than 2: - Databee Business Systems

Check if this is greater than 2: - Databee Business Systems

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 Only $ k = 0 $ gives $ x = -3 $, $ k = 1 $ gives $ x = 501 $.

📌 No two-digit solution.

📌 But perhaps we made a misinterpretation. Let’s suppose the question means a number that is **three less than a common multiple** of $ 7, 8, 9 $, not necessarily the LCM.

📌 So $ x + 3 = \text{lcm}(7,8,9) \cdot k = 504k $.

📌 Still same result.

📌 Alternatively, maybe the question meant **three less than a multiple of each**, not the same multiple. But that would be ambiguous.

📌 But let’s reconsider: perhaps the intended LCM was miscalculated.

📌 Wait: $ \text{lcm}(7,8,9) $:

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Solution: We are to minimize $ rac{1}{a} + rac{1}{b} + rac{1}{c} $...
By the AM-HM inequality:
rac{a + b + c}{3} \geq rac{3}{rac{1}{a} + rac{1}{b} + rac{1}{c}} \...
Taking reciprocals (since all terms are positive):
rac{1}{a} + rac{1}{b} + rac{1}{c} \geq 9
Equality occurs when $ a = b = c = rac{1}{3} $. Thus, the minimum val...
Question: Let $ h(x) $ be a polynomial such that $ h(x^3 + 1) = x^6 +...
Solution: Observe that the right-hand side is $ (x^3 + 1)^2 + 2 $. How...
h(x^3 + 1) = (x^3 + 1)^2 + 2 \Rightarrow h(u) = u^2 + 2
Then, substitute $ u = x^3 - 1 $:

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