Beautiful But So Dangerous
Algebra
Level
4
\[ \small \frac{x^3y^4z^3}{(x^4+y^4)(xy+z^2)^3}+\frac{y^3z^4x^3}{(y^4+z^4)(yz+x^2)^3}+\frac{z^3x^4y^3}{(z^4+x^4)(zx+y^2)^3}\]
Over all positive reals \(x, y \) and \(z\), the maximum of the expression above can be expressed as \(\dfrac{m}{n}\), where \(m\) and \(n\) are coprime positive integers. Find \(m+n\).
Source: VMO 2014 problem 2 day 2.
by
MS HT