# Problem 22

Algebra Level 5

$\large \left( \frac{x}{y}+\frac{y}{z}+\frac{z}{x} \right)^3 + \frac{525(xy+yz+xz)}{x^2+y^2+z^2}$

If $$x,y,z$$ are positive real numbers, the minimum value of the above expression can be expressed as $$\frac{m}{n}$$ where $$m,n$$ are positive integers that are relatively prime. Find $$m+n$$.

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