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0211 inequalities 2nd edition Round 1 p1

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May 10, 2021
inequalities2nd edition

Problem Statement

Let x,y,zx, y, z be positive numbers such that xyz≤2xyz \le 2 and 1x2+1y2+1z2<k\frac{1}{x^2}+ \frac{1}{y^2}+ \frac{1}{z^2}< k, for some real k≥2k \ge 2. Find all values of kk such that the conditions above imply that there exist a triangle having the side-lengths x,y,zx, y, z.
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