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Find all pairs (a, b)

Source: 2020 Austrian Mathematical Olympiad Junior Regional Competition , Problem 1

June 7, 2020
algebrainequalitiesHigh school olympiadAustria

Problem Statement

Let aa be a real number and bb a real number with b≠−1b\neq-1 and b≠0.b\neq0. Find all pairs (a,b) (a, b) such that (1+a)21+b≤1+a2b.\frac{(1 + a)^2 }{1 + b}\leq 1 + \frac{a^2}{b}. For which pairs (a, b) does equality apply? (Walther Janous)
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