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The real numbers a,b,c,x,y,za , b , c , x , y , za,b,c,x,y,z satisfy a≥b≥c>0a\geq b \geq c > 0a≥b≥c>0 and x≥y≥z>0 x \geq y \geq z >0x≥y≥z>0
The minimum value of
(ax)2(by+cz)(bz+cy)+(by)2(cz+ax)(cx+az)+(cz)2(ax+by)(ay+bx) {\dfrac{(ax)^{2}}{(by + cz)(bz + cy)}} + {\dfrac{(by)^{2}}{(cz + ax)(cx + az)}} + {\dfrac{(cz)^{2}}{(ax + by)(ay + bx)}} (by+cz)(bz+cy)(ax)2+(cz+ax)(cx+az)(by)2+(ax+by)(ay+bx)(cz)2
can be expressed as mn \frac{m}{n} nm, where mmm and nnn are positive coprime integers. Find 50(m+n) 50(m + n)50(m+n)
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