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Problem 2 -- Four Variables' Inequality Adventure

Source: 47th Austrian Mathematical Olympiad Regional Competition Problem 2

July 27, 2018
inequalitiesAustriaalgebra

Problem Statement

Let aa, bb, cc and dd be real numbers with a2+b2+c2+d2=4a^2 + b^2 + c^2 + d^2 = 4. Prove that the inequality (a+2)(b+2)≥cd(a+2)(b+2) \ge cd holds and give four numbers aa, bb, cc and dd such that equality holds.
(Walther Janous)
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