lean_workbook_plus_48859

With $x_1=21$ , $x_2=17$ , $x_3=16$ , $x_4=14$ , again with $x_1^2$ , $x_2^2$ , $x_3^2$ , $x_4^2$ being the sides of a quadrilateral, gives $4(\frac{x_{1}}{x_{2}}+\frac{x_{2}}{x_{3}}+\frac{x_{3}}{x_{4}}+\frac{x_{4}}{x_{1}}) - (x_{1}+x_{2}+x_{3}+x_{4})(\frac{1}{x_{1}}+\frac{1}{x_{2}}+\frac{1}{x_{3}}+\frac{1}{x_{4}}) =\frac{10}{119}>0$