FI-MO 2014 Problem 1

Determine the value of the expression $x^2 + y^2 + z^2$ ,

if $x + y + z = 13$ , $xyz= 72$ and $\frac1x + \frac1y + \frac1z = \frac34$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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