Cauchy-Schwarz: Problema 8

Let \(a,b,c,x,y,z\) be reals such that \((a+b+c)(x+y+z)=3\) and \((a^{2}+b^{2}+c^{2})(x^{2}+y^{2}+z^{2})=4.\) Prove that \(ax+by+cz
\geq 0.\)

Vasile Cîrtoaje