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least possible alpha

Source: Romanian District Olympiad, grade 10, p1

March 10, 2024
algebrafunction

Problem Statement

Let a,b∈R, a>1, b>0.a,b\in\mathbb{R},~a>1,~b>0. Find the least possible value for α\alpha such that :(a+b)x≥ax+b, (∀)x≥α.(a+b)^x\geq a^x+b,~(\forall)x\geq\alpha.
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