Track / Stage 6 / 171 of 400 #1171 of 2000

Problem 1171

National olympiad, first round

Algebra Difficulty 6.3 Prove it

83. Let $a, b, c, d$ be positive real numbers, and $a+b+c+d=4$ , prove: $\frac{1}{5-abc}+\frac{1}{5-bcd}+\frac{1}{5-cda}+\frac{1}{5-dab} \leq 1$ (Vasile Cirtoaje)

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

Official solution

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.