Question 69
(YUG 1) Suppose that positive real numbers $x_1,x_2,x_3$ satisfy
$$x_1x_2x_3>1,\qquad x_1+x_2+x_3<\frac1{x_1}+\frac1{x_2}+\frac1{x_3}.$$
Prove that:
(a) None of $x_1,x_2,x_3$ equals $1$.
(b) Exactly one of these numbers is less than $1$.
$$x_1x_2x_3>1,\qquad x_1+x_2+x_3<\frac1{x_1}+\frac1{x_2}+\frac1{x_3}.$$
Prove that:
(a) None of $x_1,x_2,x_3$ equals $1$.
(b) Exactly one of these numbers is less than $1$.