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1

Part of 2022 Austrian MO Regional Competition

Problems(1)

1/(1-a)+ 1/(1-b) >= 4 if a,b>0 with a^2 + b^2 =1/2

Source: 2022 Austrian Regional Competition For Advanced Students p1

10/4/2022
Let aa and bb be positive real numbers with a2+b2=12a^2 + b^2 =\frac12. Prove that 11−a+11−b≥4.\frac{1}{1 - a}+\frac{1}{1-b}\ge 4. When does equality hold?
(Walther Janous)
algebrainequalities