Beautiful But So Dangerous

Algebra Level 4

x3y4z3(x4+y4)(xy+z2)3+y3z4x3(y4+z4)(yz+x2)3+z3x4y3(z4+x4)(zx+y2)3 \small \frac{x^3y^4z^3}{(x^4+y^4)(xy+z^2)^3}+\frac{y^3z^4x^3}{(y^4+z^4)(yz+x^2)^3}+\frac{z^3x^4y^3}{(z^4+x^4)(zx+y^2)^3}

Over all positive reals x,yx, y and zz, the maximum of the expression above can be expressed as mn\dfrac{m}{n}, where mm and nn are coprime positive integers. Find m+nm+n.


Source: VMO 2014 problem 2 day 2.
×

Problem Loading...

Note Loading...

Set Loading...