Problem
A three-variable inequality
Prove a symmetric inequality for arbitrary real x, y, and z.
For all real numbers \(x,y,z\), prove that
\[\begin{aligned} &(x^2+yz)(y^2+zx)(z^2+xy)\\ &\qquad\leq (x^2+y^2)(y^2+z^2)(z^2+x^2). \end{aligned}\]The variables may be positive, zero, or negative.
No solution is included with this problem.