How one can use Sagemath to prove that $\frac{x}{\sqrt{y^2 + 15 xz}} + \frac{y}{\sqrt{z^2 + 15 xy}} + \frac{z}{\sqrt{x^2 + 15 zy}}\geq \frac{3}{4}$ for all $x>0, y>0, z>0?$
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How one can use Sagemath to prove that $\frac{x}{\sqrt{y^2 + 15 xz}} + \frac{y}{\sqrt{z^2 + 15 xy}} + \frac{z}{\sqrt{x^2 + 15 zy}}\geq \frac{3}{4}$ for all $x>0, y>0, z>0?$
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