Question 82
The nonnegative real numbers $x, y, z$ are such that $(x + y)(y+z)(z+x) = 1$. We denote by $m$ and $M$ respectively the smallest and largest possible values of the expression $A = (xy + yz + zx)(x + y + z)$.
a) Find $m$ and $M$.
b) Is there a triple of nonnegative rational numbers $(x, y, z)$ satisfying the given equality for which $A = m$?
a) Find $m$ and $M$.
b) Is there a triple of nonnegative rational numbers $(x, y, z)$ satisfying the given equality for which $A = m$?