Titu's, CS, or Something Else?

Algebra Level 4

The real numbers a,b,c,x,y,za , b , c , x , y , z satisfy abc>0a\geq b \geq c > 0 and xyz>0 x \geq y \geq 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)}}

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

×

Problem Loading...

Note Loading...

Set Loading...