Algebra · Inequalities · Am gm · Cyclic constraints · Constrained minimum · Equality case
Find the smallest possible value of \(x + y + z\) for non-negative real numbers \(x, y, z\) subject to
\[ \begin{aligned} xy(10x + 10y + 7z) &\geq 27, \\ yz(10y + 10z + 7x) &\geq 27, \\ zx(10z + 10x + 7y) &\geq 27. \end{aligned} \]
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Serbian National Competition (Drzavno takmicenje) 2007, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source