Track / Stage 6 / 163 of 400 #1163 of 2000

Problem 1163

National olympiad, first round

Algebra Difficulty 6.2 Prove it

Example 7 Let $x, y, z$ be non-negative real numbers, and $x+y+z=1$ , prove: $0 \leqslant y z+z x+x y- 2 x y z \leqslant \frac{7}{27}$ . (25th IMO Problem)

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.