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 \( 50(m + n)\)
by
U Z