# Titu's, CS, or Something Else?

Algebra Level 4

The real numbers $$a , b , c , x , y , z$$ satisfy $$a\geq b \geq c > 0$$ and $$x \geq y \geq z >0$$

The minimum value of

${\dfrac{(ax)^{2}}{(by + cz)(bz + cy)}} + {\dfrac{(by)^{2}}{(cz + ax)(cx + az)}} + {\dfrac{(cz)^{2}}{(ax + by)(ay + bx)}}$

can be expressed as $$\frac{m}{n}$$, where $$m$$ and $$n$$ are positive coprime integers. Find $$50(m + n)$$

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