AUSTRIAN-POLISH 1996 Problem 4

Real numbers $x,y,z, t$ satisfy $x + y + z +t = 0$ and $x^2+ y^2+ z^2+t^2 = 1$ .

Prove that $- 1 \le xy + yz + zt + tx \le 0$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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